Looking Back Over My Shoulder

The start of a new year (or the end of the previous one) is a time for looking forward, setting goals making resolutions and planning for the future. There's a general view that looking back isn't healthy and focusing on the past doesn't create a healthy mindset.  This is often the case if the previous year has been difficult, challenging or simply awful.

I disagree.

Looking back at the past can help us identify our strengths, our victories and how we can build on them.

The shepherd boy David took on the giant Goliath. He volunteered, based on his previous experience and his previous victories with God.  He knew his God; he knew his place and he knew his own history.

1 Samuel 17:
34But David said to Saul, “Your servant has been keeping his father’s sheep. When a lion or a bear came and carried off a sheep from the flock, 35I went after it, struck it and rescued the sheep from its mouth. When it turned on me, I seized it by its hair, struck it and killed it. 36Your servant has killed both the lion and the bear; this uncircumcised Philistine will be like one of them, because he has defied the armies of the living God. 37The Lord who rescued me from the paw of the lion and the paw of the bear will rescue me from the hand of this Philistine.”

David had learned from his experiences with God, conquering lions and bears in previous years, and he used this experience with 'small things' in preparation for his next challenge.

So, look back over your shoulder, take stock and review your victories, your experience and the positives. Carry them with you (like a sling and a staff) and go take on your giants!

Just: Not Good Enough

I don't make many New Year's Resolutions.  Truth is, I'm still working through my resolutions from a few years ago: to give more than I receive; to repair not replace and so on.

This year, I have one resolution that I've already started on.  Simply put, Just: Not Good Enough.

"Daddy, come and play with me!'
'I'm just washing the dishes.'
'Just give me a second, I'm just tidying the floor.'
'I'm just sending an email.'
'I'm just checking Facebook'.

And so on.

So this year, I'm going to stop saying "just". If I'm washing my hands, my face, the dishes or whatever, then that's what I'm doing. Saying "just" makes it less important, and makes your request to play or set up your game or whatever even less important. "Just" is not a good enough word to use.

And if you ever catch me saying "just" in my prayers, tell me. I don't usually use "just" but you never know.  Imagine:

"Mighty Father God, maker of the universe, please would you just lift my headache for half an hour."
'30 minutes? Are you sure?'
"Yes, and i pray that you would just bless the meeting at church this morning."
'And this afternoon? When you all go back home?'
"Just this morning is fine, thanks."
'Are you sure??'
"Yeah, and we just pray... that you would just..."

So, I'm going to lift the lid on what I pray for. I don't say "just" verbally when I pray, but I mentally contain God in what I ask for. I've been getting better at asking for the Moon (so to speak) and expanding what I pray for, and asking for bigger things, and this is my main aim for 2020.

Just: Not Good Enough.

2019 in reflection

At the end of 2018 I wrote a summary reflection of the year, and the theme I identified was "first times". 2019 seems to have been similar, with a surprising number of first times. However, the other main theme for the year has been change (I suppose if you do something for the first time it's either the cause or consequence of change).

My three children now all go to the same school, with our youngest moving from pre-school nursery to primary school nursery. It's a subtle distinction, but it now means that Daddy's Taxi only has to make one drop in the morning. 2020 will see our oldest child start high school, which will mean more significant changes ahead.

Planning further ahead into the future, we had a conservatory built onto the back of our house in 2019, and that led to significant change (I still don't think of it as part of our house, and it's been finished for three months now).  It's given us more living space, and in time will become my office during the daytime, as we move things around in the future.

While I was on a work experience placement from high school, the desk I was borrowing had a desk calendar with a daily motto, and one that I saw (and kept) was "Unless we know what we want ), we stand a poor chance of getting it." Over the years, that motto has helped me identify what I actually want, and to work towards it.  This year, I have taken that a step further and extended it to, "And if we don't ask for it, we really won't get it."  What do I want to drink? What would I like for dinner? What do I want to do this weekend? What do I want for Christmas? I've started changing what I say - and how I think - so that if you ask me what I want,  I'm more likely to tell you. And sometimes, it's actually up to me to say what I want to do. I'm lifting the lid on what I think I can do, or what I'm supposed to do, or what I think I'm allowed to do (usually inside my own head) and instead of discounting my own ideas myself (I could never do that), I'm at least going to say what I want first!

So, 2019 has been a year of change - internal and external - and is likely to lead to more change next year.

Happy New Year, and may you ask for what you want.

Web Analytics: Requirements Gathering

Everybody knows why your company has a website, and everybody tracks the site's KPIs.

Except that this a modern retelling of the story of three blind men who tried to describe an elephant by touch alone, and everyone has a limited and specific view of your website.  Are you tracking orders? Are you tracking revenue? Are you tracking traffic? Organic? Paid? Banner? Affiliate? Or, dare I ask, are you just tracking hits?

This siloed approach can actually work, with each person - or more likely, each team - working towards a larger common goal which can be connected to one of the site's actual KPIs.  After all, more traffic should lead to more orders, in theory.  The real problem arises when people from one team start talking to another about the success of a joint project.  Suddenly, we have an unexpected culture clash and two teams, working within the same business, are speaking virtually different languages.  The words are the same, but the definitions are different, and while everybody is using the same words, they're actually discussing very different concepts.

At this stage, it becomes essential to take a step back and take time to understand what everyone means when they use phrases like,  "KPIs","success metrics", or even "conversion". I mean, everyone knows there's one agreed definition of conversion, right? No?  Add to cart; complete order; complete a quote, or a lead-generation activity - I have seen and heard all of these called 'conversion'.

When it comes to testing, this situation can become amplified, as recipes are typically being proposed or supported by different teams with different aims.  One team's KPIs may be very different from another's.  As the testing lead, it's your responsibility to determine what the aims of the test are, and from them - and nothing else - what the KPIs are.  Yes, you can have more than one KPI, but you must then determine which KPI is actually the most important (or dare I say, "key"), and negotiate these with your stakeholders.

A range of my previous pieces of advice on testing become more critical here, as you'll need to ensure that your test recipes really do test your hypothesis, and that the metrics will test the hypothesis.  And, to avoid any doubt, make sure you actually define your success criteria in terms of basic metrics (visits, visitors, orders, revenue, page views, file downloads), so that everybody is on the same page (literally and metaphorically).

Keep everybody updated on your plans, and keep asking the obvious questions - assume as little as possible and make sure you gather all your stakeholders' ideas and requirements.  What do you want to test? Why? What do you want to measure? Why?

Yes, you might sound like an insistent three-year-old, but it will be worth it in the end!

How to Solve Edge Matching Cards Puzzles - Practical Advice

While I was at high school, around 25 years ago, I was first introduced to an edge-matching puzzle.  This is made up of 16 square card pieces, with a colour on each edge, that have to be arranged into a 4x4 square so that all the colours of the edges on each piece matches their adjacent neighbour.

It all sounds so easy.

I recently acquired two versions of this edge-matching puzzle - one based on cogs, and one based on footballers - with a view to finally solving it.  I didn't solve the puzzle while I was at school, and I've not revisited it much since, except to conclude that it was impossible, or was going to take longer to solve than I wanted to invest in it.  Well, things have changed, and as it's clearly been pestering me for 20+ years, so I figure it's time to rise to the challenge - especially since the Special Educational Needs Co-ordinator at my high school took delight in telling me that one of the 'weaker' children in our year group had successfully solved it.  Challenge accepted, Mrs Kirkham!

Here, for reference, are the 16 cards in the "Mechanical Mayhem Puzzle":

My first few attempts at the puzzle were not at all successful.  I very quickly connected a few pieces, but never made significant progress, and never really got past about 75% complete  before the pieces refused to go together any more.  I therefore decided it was time to get some hints and help, from that reliable source of all knowledge - the internet.

The most helpful information I found was from a research paper into edge-matching puzzles - apparently, these puzzles are not trivial, in fact they are N-difficult.  The advice was to find matching pairs, and then try to connect pairs to form fours, sixes and eights.  The pairs didn't always form squares, but at least I was now working systematically.  Here are a few candidate pairs, as examples:

And then some candidate squares:

As I became more familiar with the cards, I quickly identified patterns that would not work - for example there are only two squares which contain the bronze-coloured cog shown on the right.  Therefore they must form a pair, since the likelihood of them both being on the outside edge of the 4x4 square seemed low to me.  I didn't count each kind of cog and work out which were the most and least frequent, but I soon noticed that the large golden cog was very common, as was the yellow daisy-style cog.  The very small silvery cog was quite rare, so I was more careful with how I placed any cards that contained it.

And, with a little trial and error, this approach worked for me (with some adjustments, intuition and observation).  You can see from my final solution that the key pair of bronze coloured cogs are in the top-left corner, and yes, I conquered the edge-matching puzzle (and it only took me 20+ years).

Transformers Trading Card Game: Applied Probability

I've mentioned previously that I have an interest in the Transformers Trading Card Game.

It works like this:  you select a number of character cards, each with specific abilities.  You also compile a deck of 'battle' cards - at least 40, but with no upper limit - that you use to form your hand and the cards that you play in conjunction with your character cards.

Much of the skill in the game comes in deciding which characters to play together as your team, and then in deciding which battle cards you put into your deck.  The battle cards can provide weapons upgrades, armour or utilities, or they can be actions that you play to benefit your team (or to damage your opponent's team).  Each battle card can have between 0-3 coloured icons on them, which has a specific effect on your character's performance when you battle your opponent.  There are orange icons (good for attacking), blue icons (good for defending), white (lets you play more cards while battling), green icons (separate effect on the cards in your hand) and black icons (also good for attacking).

Before you play the game, you have to decide which cards you want to play, and what mix of coloured icons you want to have in your deck.  All orange is all-out attack; all blue is all-out defence; and so on.  But this is where it gets interesting:  some of your characters' special abilities rely on you getting white icons, or orange icons, or even a mix.  One of the character cards I'm working on at the moment is Mirage.  He has an ability where he can 'untap' if you can draw three white icons while he's attacking.  If you draw one white icon while attacking, then you draw two more cards - and hence have the possibility of getting more white cards, if you have a good proportion of white icon cards in your deck.  (There are other ways of drawing more cards while you attack, but that gets very complicated).

And the second - in a different team - is Grapple.  If you can flip a specific combination of cards while he's battling, you get a significant boost to your attack or defensive ability.  You can double his attack rating from 4 to 8, and improve his defence rating from 0 to 4 if you can flip cards which have EXACTLY four different coloured icons.  Duplicated icons are allowed - so flipping one white, one orange, two blue and two green is a success.  Three different colours don't count, and neither do five (if you drew a black, orange, yellow, white and green).

There is an additional property of the cards that we can use - some cards have two different coloured icons on them... white and green; green and blue; green and orange.  There are a strictly limited number of card which have three icons - typically white, orange and blue.  So the probability of hitting a successful flip are increased if I use these cards in my deck.  Computron's Lab have carried out some extensive quantitative research on the ideal deck for Grapple, which is composed entirely of blue-black and white-green, explaining that this gives the highest likelihood of drawing cards to enable Grapple's skill.  I've taken a slightly different approach:

THE GRAPPLE DECK

Grapple - 12 stars


Private Red Alert - 7 stars
Silverbolt - 5 stars

(Red Alert and Silverbolt have similar benefits to Grapple - they both activate their skills when you flip at least one white, orange and blue icon when battling).

Extra Padding:  two icon colours and Tough 1.
What's not to like?

Blue-Green = 4
Extra Padding x3
Dismantling Claw x1 (may remove this in future)

White-Green = 9
Secret Dealings x3
Spare Parts x3
Personal Targeting Drone x3

White = 6
Data Pad x3
Spinner Rims x3

Blue = 8Evasive Maneuvers x2
Inspiring Leadership x3
Reinforced Plating x3

Orange = 15
Flamethrower x3
Incoming Transmission x3
Body Armour x3
Treasure Hunt x3
Supercharge x3

and
Orange-White-Blue (although this a 'star card') = 1
Fuel Depot

Total 42

Orange: 16; Blue 13; White 16; Green 13  Total 48

The selection is almost certainly not the optimum in terms of drawing one of each of the four colours.  However, there is more than just the coloured icons to consider - some of the cards can be played to enable you to draw more cards in your turn.  The game calls this "Bold" when you're attacking, and "Tough" when you're defending.

Bold 3? Yes, please!

Flamethrower - Bold 2
Supercharge - Bold 3
Spinner Rims - Bold 1

Extra Padding - Tough 1
Evasive Maneuvers - Tough 3

Additionally, I have over-indexed on white icons, because if you can draw a card with a white icon, you get to draw two extra cards for that battle (only applies to the first white icon you draw per battle) - and I want to be as confident as possible of hitting a white icon each time.  In total, 16 of the 42 cards have a white icon; ideally I should probably have half of the cards with a white icon, to give me a higher chance of hitting one white icon in every two cards I draw.

In simulations with Bold 0 or Tough 0 (where I drew two cards - plus the two more if I flipped a white), I achieved success in almost a quarter of the draws (6/26).  When I gave myself Bold 1, drawing one extra card, I saw surprisingly little difference - a smaller sample size saw me achieve success on 2 out of 10 occasions.  I shall continue optimizing through empirical data - and because I like the idea of going 'full rainbow.  The research continues.

"A Puzzle A Day" - Sum of three numbers equals their product

Puzzle 84:
Mr Puzzle says there is only one unique set of three numbers whose total (added together) is equal to their product (multiplied together).  What is it?

This puzzle reminds me of the recent question - "What three numbers satisfy 1/a + 1/b + 1/c = 1?", where the answer was 1/2 + 1/3 + 1/6 = 1.  

The answer to a + b + c = abc can be found if you know that 6 is a 'magic' number - the sum of its factors is equal to their product.

The factors of 6 are 1, 2 and 3:   1 + 2 + 3 =  6 = 1 * 2 * 3

6 is a perfect number  - it's equal to the sum of its divisors (except itself).  Another example is 28 (1 + 2 + 4 + 7 + 14); there are plenty more perfect numbers, and they are extremely large.

6, also is a magic number - it's equal to the product of its divisors (again, except itself).  I can't find any other examples - I guess 6 is unique.  Well, that's what Mr Puzzle said, anyway.

Port Vale 1 Cambridge Utd 0

At the end of the last school year, our family was fortunate enough to win a pair of tickets (one adult and one child) to any one Port Vale home match of the 2019-2020 season. My wife has zero interest in football (possibly even less than that), and one of my children loves football, one has no interest and one is too young to appreciate it. So Lizzie and I won by default, and I opted for the home game against Cambridge United on Saturday 31 August.

This, like my report from Port Vale vs Stevenage from a few years ago (February 2011!), is more of an eyewitness report than match analysis.

The game started brightly under blue, cloudy skies. Vale had some very early chances and most of the early pressure.  The team played well and the majority of the first 45 minutes was played in Cambridge's half.  I don't recall Cambridge having any first-half chances, and it was mostly one-way traffic.

A couple of rare attacks along Cambridge's right wing were stopped by some strong physical defending, as the Vale left back and centre back were pushed, pulled back and occasionally got into a tussle with shirts being pulled and so on.

Nathan Smith (left) keeps an eye on Sam Smith (centre)

There was a period in the first half where the game threatened to boil over, and here I must blame the referee, who (in my own unqualified opinion) had a poor game. He missed a lot of the pushing and shoving that I've mentioned - from both sides - and failed to make the bookings that would probably have calmed things down and reminded the players of the rules.  Port Vale's Nathan Smith was involved in a number of physical challenges against Cambridge attacker Sam Smith, and they both (in my view) came close to getting booked.  

Port Vale continued to press, but the players went in at half time with no goals scored. Some of the fans near us viewed this as a glass-half-full situation, since Vale hadn't conceded either, and were on track for their first clean sheet of the season.

The referee didn't make any bookings during the first half, and consequently in the second half the game came very close to boiling over. 

The referee attempts to deal with a scuffle
without getting directly involved.

The referee steps into another scuffle, but note the two players behind him STILL fighting over the ball.

One petty incident involved a minor controversial scuffle - did he slip or was he pushed? - and one of the Cambridge players landed on the ball and  stopped to pick the ball up as he was certain he'd been fouled.  The Vale defenders argued that he hadn't been fouled, and had subsequently handled the ball immediately.  A scrum of around seven or eight players followed, each side determined to get hold of the ball (literally). The referee failed to take charge of the situation, and remained an almost impassive bystander, only booking one or two of the players, when other officials may have gone further.  It's always unfortunate when a referee manages to get himself noticed through his decisions - this was one of those games.

Cambridge United started the second half much more brightly and energetically and started gaining chances, but did not convert any of them.  As the game opened up, Vale were able to make some headway down both wings. David Amoo constantly made his presence felt in the inside right position, and kept threatening to beat the Cambridge defence.  

On the left wing, David Worrall was not having a great game.  His work rate was excellent, chasing down any opportunities on the Vale left, but he failed to make any progress and his crosses were all easily collected by the Cambridge goalkeeper, Dimitar Mitov.  Vale won a quick series of corners on the left hand side as the second half went on, but none of them produced any real chances, with Mitov proving excellent in goal and easily collecting any of the high crosses into the box. 

On the right wing, there were some nice tight passing sequences as the Vale attack attempted to break down Cambridge's deep and persistent defence, and it was through the right wing that Vale eventually got their winner.  David Amoo was able to break forwards and beat two defenders on his way into the Cambridge area; he got close to the by-line and sent a fast, low cross across the face of the goalmouth.
  

Retreating defender Davies beat his own goalkeeper to the ball and turned it in to the goal for an unfortunate own-goal.  Vale were able to hold on to their lead for the final five minutes (plus stoppage time) and also achieved their first clean sheet of the season, so it was a double winner that consolidated their mid-table position and allowed them to set their sights on the top half of the table.

 

Star Trek Discovery - First Impressions

Now I know I am a little late to the party, but our household recently started a Netflix subscription (primarily because we has just finished Parks and Recreation from start to end) and Mrs Leese had seen clips of Brooklyn 99 on YouTube. Brooklyn 99 is only available through Netflix, so that was that - we subscribed to Netflix.

An additional benefit is that Netflix streams Star Trek Discovery. It wasn't my idea to subscribe to Netflix, but I am not complaining!

Star Trek Discovery is the first new Star Trek series I've seen since Enterprise, and a lot has changed since then - 9/11, ISIS, the discovery of the Higgs Boson... it's a whole new world.  Star Trek has kept pace with changes in sci fi TV visuals, in the same way as the rebooted films have presented the best of Hollywood's visual effects.  But what about the audience? While Enterprise was airing in the UK, I was recording episodes on VHS video cassettes, so that I could watch episodes either live or at a time after their original air date.  It took weeks and months to get through a series (season), and by the end of a season  you could watch the series from end to end and better see the threads in the plot - if there were any.  Star Trek was entirely episodic, so you knew everything would be back to normal by the end of the hour.  In fact, season 3 of Enterprise (the Xindi arc) was widely criticised because it ran as a season-long arc and you couldn't just watch an episode in isolation (there were a few that could stand alone, but not many).

Now, with streaming services delivering on-demand TV 24/7/365, it's possible to watch Season 3 of Enterprise in a day. Not sure you'd want to, but the possibility exists.

Star Trek Discovery is able to balance the episodic nature of Star Trek with the demands of modern streaming audiences. The first two episodes are best viewed back-to-back, in the same way as TNG, DS9, Voyager and Enterprise all started with two-parters. There is a clear arc set up - the start and execution of the Klingon War - and then there are some serious differences. Observant viewers will notice that the series is called Star Trek Discovery, but the episodes start on the Shenzou. And the Captain is played by Special Guest Star Michelle Yeoh, who, as a Hollywood film actress is unlikely to be sticking around for the series. I predicted the destruction of the Shenzou with the captain on board before the opening credits had even finished.


Not that I'm complaining. The story shows us life in the Federation from the perspective of a mutinous officer who has only been saved from the brig and eventual court martial and expulsion by the needs of war.  Star Trek hasn't had a criminal in the crew since Tom Paris was pardoned and allowed to join the Voyager crew, and Lt Suder fought his violent tendencies while trying to integrate into the same crew.  This allows for some wonderful character interaction as the crew realise that they have Michael Burnham (famous mutineer) on board.  Meeting the crew from Michael's perspective means that we're thrown into the middle of a fully integrated crew - there's no shakedown time.  

The characters and names in this story are entirely fictitious. 
Any resemblance to any persons living or dead...

This is more TNG than Voyager, for sure.  Voyager started with the death of the second officer, the chief medical officer and the conn officer, throwing the Maquis and the Federation crews together.  There's none of that here; this is an established crew  who already know each other - and we don't.  The officer with the eye-enhancement (Keyla Detmar), who bears no resemblance to Seven Of Nine; the bridge officer who looks like a relative of Nebula from Guardians of the Galaxy (Airiam) - we know very little about them, except that they're bridge officers. Still, there's plenty of time for the series to show us more about them, all in good time.

...is entirely coincidental.

So far, I have watched the first seven episodes, up to and including Magic to Make The Sanest Man Go Mad, and I am pleased to say I have thoroughly enjoyed a very new, fresh angle on the Star Trek universe. The crew have a healthy smattering of imperfections and character flaws; and when placed in a stressful war scenario, these imperfections become exposed .  The writers are not afraid to kill off characters and destroy ships with alarming frequency (the captain of the Shenzou is one example).

And there's a great balance between episodic and arcing TV. In episode five, Choose Your Pain, we meet Harry Mudd (who will go on to become a thorn in James T Kirk's side). By the end of the nearly wrapped episode, he's left to to rot in a Klingon prison, and that's a neat and tidy conclusion.  But oh, no, he's back again in the standout episode seven, Magic to Make The Sanest Man Go Mad, and he wants revenge.  Again we have another episode which reaches a firm conclusion, but now we're also wondering how long it will be before he'll be back again.

There are a few minor drawbacks to the way the story has been set up, the most noticeable being that as a prequel, we know how the story is going to end - there's no spore drive in Kirk's universe, so the ship is probably going to get destroyed eventually.  I just hope it doesn't get erased from the timeline completely ("And Spock woke up and realised it was all a dream"? No thanks).

Otherwise, I am thoroughly enjoying the new series and can wholeheartedly recommend it.

"A Puzzle A Day" - Flowers, and Venn Diagrams

The next puzzle can be solved longhand, but the best tool I would recommend is a Venn diagram, which solves the puzzle and elegantly shows your working (which my maths teachers said was always a good thing).

"Betty was making paper flowers for the local carnival.  11 flowers had red in them, seven had yellow in them, and five had red and yellow in them.  How many flowers did she make?"

The short answer (11+7+5 = 23) is incorrect; the point here is that the 11 flowers with red in them includes the five that had both red and yellow in them.  Similarly, the seven yellow flowers includes the five that had red in as well.

The quickest way to solve this is with a Venn diagram - see below.  Each circle contains the number of flowers of that colour, and the overlap shows the number of flowers which contain both red and yellow.

We know that there are five flowers which have both colours in them, so we can write 5 in the intersection (overlap) point of the two circles.  We also know that the red circle in total must contain 11 flowers, so the area outside the overlapping section is 11-5.  Finally, for the yellow the circle, the total needs be 7.

Simplifying this, we can see that there are 6 flowers that are red-only, 2 that are yellow-only, and five that are both red and yellow:

And hence the total is 13.  The initial "23" (11+7+5) counts the overlapped area twice more than it should be (i.e. it's counted as a red flower, a yellow flower and as a red-and-yellow flower).  By drawing out a simple Venn diagram, it's easy to see what the correct solution is.

"A Puzzle A Day" - add nine, reverse digits

This puzzle is one of those which is almost as simple to solve as it is to state:

Find a two-digit number that reverses its digits when you add nine to it.

Knowing that the nine-times table contains numbers which have two series of ascending tens and descending units, this should be a case of just identifying a pair:

9, 18, 27, 36, 45, 54, 63, etc.

However, there are many more pairs of numbers that fit the requirement in the question:

23 and 32
34 and 43
45 and 54 we've already mentioned
56 and 65
and so on

Any two digit number of the form (10x + (x+1)) or 11x+1 will reverse its digits when adding nine (up to 89 + 9 = 98).

The situation changes above 100, and its not possible to reverse digits by adding just nine (and we have three-digit numbers).

"A Puzzle A Day" - How Old Is Aunt Tabitha (age in days)

Next puzzle - another interesting one: 

Aunt Tabitha was extremely touch about her age.  When an impudent nephew was brave enough to ask her, she cunningly replied that she was 35 years old, not counting Saturdays or Sundays.  How old was she?

So Aunt Tabitha has given her age in weekdays, and weekdays only account for five-sevenths of the total week.  Therefore, Aunt Tabitha's stated age of 35 is only five-sevenths of her actual age; 35 / (5/7) = 49.

So she's 49 years old.  But I'll leave it to the impudent nephew tell her that.

It might have been more interesting if she'd given her age as 14 years old in weekends - which is also a more exciting and appealing way of describing her age.

Having said all that, I can say that I'm 30 years old (excluding weekends), or, even better, 12 years old in weekends.  I'm not touchy about my age, but the thought of being 12 years old in weekends (and not even a teenager) is definitely more appealing than stating my actual age!

"A Puzzle A Day" - A Three Horse Race

This puzzle comes from the Puzzle A Day pad (it's meant to last a year; at this rate I'll be completing it in 2025).

The question is simple (but with a slight twist):  "How many ways can a three horse race finish, including ties?"

The simple answer (excluding ties) can be found by looking at all the possible combinations; if we call the horses A, B and C, then we have:

ABC
ACB
BAC
BCA
CAB
CBA

Six ways.

Now, refreshing the list and including the ties (which will be shown in brackets):

ABC
A(BC)
(AB)C
ACB
A(CB)
(AC)B
BAC
B(AC)
(BA)C
BCA
B(CA)

(BC)A

CAB
(CA)B
C(AB)

CBA
(CB)A
C(BA)
(CAB)

13 in total - there are three variations for each of the previous combinations, so ABC now becomes ABC, (AB)C and A(BC) - but we must now deduplicate A(BC) and A (CB), and so on.  The red text above shows a duplicate of a combination which has already been seen above it in the list.

And there's one where all three tie together (ABC).  The need to deduplicate the ties makes this question more complex than it appears at first sight, and so (as is often the case) care is taken to fully understand the question.

"A Puzzle A Day" inspired by Prof Rubik: Big Ben Strikes Twelve

I've recently bought a "Puzzle a Day" - it's a block of 365 single-sheet puzzles (intended to be one a day for a year) on a charity shop visit.  It was new and unopened (I should have taken the hint and walked away immediately), but I thought it might stretch my brain in new ways, and some of them will probably be blog-worthy.

Some are, some aren't.

The first couple don't translate well to a blog article, but Puzzle 3 is interesting: 

"If it takes Big Ben six seconds to strike six o'clock, how long will it take to strike twelve o'clock?"

The immediate (and wrong) answer is twelve seconds; the trick is this:  there is no time to be measured after the sixth ring.  The duration of the rings is not one second between the first and second, then another between the 2nd and 3rd, 3rd and 4th, 4th and 5th, 5th and sixth, and then a second after the sixth ring.  In fact, there are six fifths (1.2 seconds) between each chime. The sixth chime occurs after the previous five have rung out, = 5 * 1.2 seconds = 6 seconds.

Now that we know that there are 1.2 seconds between each chime, we need to calculate the length of 11 chimes (knowing that the 12th chime will occur immediately afterwards).

11 * 1.2 = 13.2 seconds, or 13 1/5 seconds.

Not 12 seconds (as you may have immediately guessed).

Sorry ;-)

Transformers Trading Card Game: Data Analysis

After my previous post, where I started playing the Transformers Trading Card Game, I started looking at the types of battle cards and doing some back-of-the-envelope data analysis.  I don't expect to find any trends, but I wanted to take a look at how the battle cards break down by type (colour, and action vs upgrade, and type of upgrade).

In my previous post, I carried out some quick high-level analysis: how many of each type of card are there?

I was surprised to see that more than half of the cards are in the Action group, while less than one in eight is Armour.  It certainly made me pay more attention to the cards I was choosing for my deck, and to consider the types of cards I was using (and not just if they would be fun to play - in theory).

Let's break them down further - what colour icons do the cards have?  White; blue; orange or green?

I know tables aren't to everybody's liking, but here's a quick, simple table that breaks down the card colours and types:

Some thoughts (from a data perspective)

- There's an approximately equal quantity of pure blue cards and pure orange cards (46 and 48); twice as many as pure white (24).  
-  White is only combined with green, not with blue or orange.  That makes sense from a game-play perspective; when attacking or defending, it would be too much to get the benefit of an orange (or a blue) and then also draw two extra cards to further add to your total.
- There are three cards which are blue/orange (an interesting and useful combination in the game); these are Recon System (which is a star card); Matrix of Leadership (can be used only on Autobots) and Roll Out!

Now, these are all great cards since they provide both defence and offence boosts.

- It is possible, but not necessarily desired, to play all white; all blue; all orange; or all blank (no icons) - any row that sums to 14 or more will produce a complete deck of that type.  There has been a lot of play with all-blue (or mostly blue) 'defensive' decks, and all or mostly orange "aggressive" or "aggro" decks.  My personal preference is towards a mixed deck with a lot of white, but I'm still working on it (I'm looking to play Mirage; Hound and Jazz, and other 'white-friendly' teams).

Wave 3 of the Transformers TCG is coming up in less than two weeks, so I'll probably be doing further analysis on how the overall card profile changes.  I'm personally looking to get the new Red Alert (with his liking for mixed decks) and Private Stakeout (who likes white), and to play them with Hound and Jazz; or Mirage/Bumblebee BW/Jazz/Private Stakeout.  We'll see!

Transformers Trading Card Game: A Newbie's View

I have long been a fan of Transformers.  I was in the target audience age of 6-10 when the first comics came out, and my first issue was issue 4, back in November 1984.  I was delighted (but mostly interested and curious) when I learned of the Transformers Trading Card Game a few months ago, and after watching quite a few YouTube videos, decided to take the plunge and buy some of the cards on eBay.  It's all relative, but £4 for a pack of cards seems expensive, while buying one or two on eBay seemed less so. 

I was impressed with the size, colouring and designs (very reminiscent of G1), so I bought a starter pack (Wave 1 Autobots), and tried my first player-versus-player match with the starter pack cards (I played both players), working through the game mechanics, keeping track of damage with a notepad and pencil, and observing while playing.  I'm no expert at card games (this is my first, and will be my only), but I started to notice a few issues with the way I was playing.

A brief summary of my first game: 

Decepticons:  Flamewar, Starscream (Scheming Second in Command), Megatron (Decepticon Leader)

Autobots:
Autobot Hound; Optimus Prime (Autobot Leader); Bumblebee (Courageous Scout)

The Autobots took a pounding due to Megatron's pierce ability; Optimus and Bumblebee were KO'd with just two turns.  Autobot Hound lasted a little longer due to his better health and I was able to repair damage from him a couple of times.  It was a narrow Autobot victory.

In between games 1 and 2, I purchased an additional 58 battle cards - a mix so that I can understand what style suits me, and what I need to play.  I also purchase the Stunticons, so I make sure I have the relevant Stunticon cards to form Menasor.

Game two
Changes from previous game: 

Decepticons 
Exchange Starscream (SSIC) for Ramjet;

Autobots change to Dinobot Swoop (Fearsome Flyer), Optimus Prime (Freedom Fighter)and Optimus Prime (Autobot Leader). 

I modify the decks to make the Decepticon deck more aggressive, while the Autobot deck includes cards like Fling, Field Repair and Repair Bay so that I can last longer in battles (in theory).  At this point I'm still not overly worried about the colours of the icons, I'm just selecting battle cards based on their abilities.

There were a number of issues I had while playing the game here:
- I was getting handfuls of action cards and almost no upgrades.  The action cards enabling me to "Play an upgrade" were useless, and the ability to play an upgrade each turn was being wasted
 - The other hands I were playing ran out of cards.  I wasn't drawing enough  - and this makes sense:  if I can only draw a card, but play an action and an upgrade, I was going to be decreasing my hand by one card per turn until I ran out.  I needed more draw capability.

I did some analysis of the overall cards in Waves 1 and Wave 2, just as a brief diversion:  There are 172 battle cards in total, of which some are duplicates.  I'll produce a deduplicated list another time:
90 (over half) are Action cards
31 are Utilities (and I was not putting enough of these in my decks)
30 are Weapons
21 are Armour

Just based on random sampling, it was no wonder that I was running out of upgrade cards (with so many action cards to choose), and then running out of cards altogether.  I had to re-balance my decks to include more upgrades and fewer actions.

And I needed more draw capability.

Game three
Decepticon PowerHouse versus Mixed Drawers

Decepticons
Megatron (Decepticon Leader)
Ramjet (Sky Smasher) - who needs abilities when you have 7 attack and 14 health?
Flamewar  - a trusty sidekick who brings the star count up to 25

Mixed DrawersAutobot Hound (Long Range Scout) - when you flit to alt mode, possibility to scrap one and draw two
Optimus Prime (Autobot Leader) - when you flit to alt mode, draw a card
Dead End - when you flip to bot mode, draw a card
Decepticon Drag Strip - brings the total to 25 stars; and when attacking in alt mode and you get a blue and orange icon, draw 2 cards.

Results
Better.  Ramjet and Megatron are still lethal, especially when given upgrades (Ramjet especially, as he has no abilities of his own).  I drew a "Disarm" for the Mixed Drawers, which ended Ramjet's resistance, and they eventually won.  I like that card!

I know I'm probably playing a biased game, but it's not completely deliberate.  I'm just subconsciously rooting for Optimus and Hound (my favourite G1 characters).

Questions

However, all this single-handed playing has led me to ask some questions:

1. How do you (as a player) select your characters and battle cards?  Do you pick characters with cool abilities, and then build a deck around them?  Or do you look at the battle cards and think "That would be fun, if I could find the right mêlée/ranged/leader character to play it with"?

2.  How do you balance the proportion of actions/armour/utilities/weapons?  What split do you use?

3.  How do you increase your draw capacity?  Cards, or flip abilities?

My ongoing battle card deck

This is still a work in progress, but here's what I'm going to try in my next game

Actions
Inspiring Leadership x3
Repair Bay x3  (actually, I only own 2 at the moment... need to fix this!)
Rest and Relaxation x3 (I know it's a green icon, but that much repair is very useful)
Fling x2
Field Repair x2
Treasure Hunt x2 (still upping my upgrade count)
Disarm x2 (this was a killer against Ramjet and I liked playing it)

Armour
Evasive Maneuvers x2
Body Armor x2
Scrapper Gauntlets x3
Reinforced Plating x2
Cooling Vents x2

Weapons
Grenade Launcher x2
Handheld Blaster x2
Enforcement Batons x2

Utilities
Debilitating Crystal x2
Security Console x2
Data Pad x2

17 Actions
11 Armour
6 Weapons
6 Utilities
40 total.

Any thoughts?