Legoland Windsor Resort Hotel

My family and I recently spent two nights at Legoland Windsor Resort's new hotel - it opened on Friday 16 March and we visited it from 19-21 March, just a few days after it had opened.  We enjoyed it so much that I decided to write a full review of our stay, including the good bits (and some of the less-good bits, although there weren't that many).

The hotel is ideal for young children.  Our two children, Lizzie (nearly 3) and Ben (nine months) both enjoyed it, even though Ben is still quite young for Lego.  The whole Legoland hotel and park has been designed to make it family friendly - for example:

The drive off the main road onto the park complex goes straight to the front door of the hotel.  There's no joining a queue of cars heading for the park - you are fast-tracked to the hotel's front door, with the hotel car park directly opposite.  The front of the hotel gives you an indication of what to expect from the rest of your stay. 


The dragon which sits in the tower above the main covered area outside the front door of the Legoland Windsor Resort Hotel also breathes smoke from time to time (I didn't work out how frequently, or if it was regularly).  It happens with loads of rumbling and growling sounds, so when you see and hear it, you know the rest of your stay at Legoland is going to be a fun time.


The Legoland hotel has four themes - adventurer, kingdom, pirate and the other one.  Each floor has its own dedicated theme, with the corridors, rooms and decor all in keeping with the theme.  Lizzie chose the Pirate theme, and thoroughy enjoyed it.

The hotel's foyer is almost wall-to-wall Lego, and this is another aspect of the child-friendly design.  There's a pit of Lego 2x4 bricks to play in (similar to the one seen at the Legoland Discovery Centre in Manchester), and a large display of over-size Lego-built minifigures, along with a large, rotating mobile containing hints as to all the rides in the Legoland theme park.  This is ideally placed in the foyer area, and is ideal for occupying the children while you go through the check-in and check-out processes.  Lizzie really enjoyed getting involved with the bricks, Ben was happy to sit in his pushchair and look at all the displays on the walls and ceiling.

One feature that deserves special comment is the whoopee cushion in the carpet...  Lizzie loved it, as you can see!


The hotel rooms are amazing; there are three floors of rooms, and each one is Legoland-themed:  Pirates, Kingdom or Adventurer.  The wall coverings, carpets, decor and even the bed linen all correspond with the theme, and you feel immersed in it.  It's very clever branding by Lego too, as there are minifigure pictures everywhere - models in the corridor areas, pictures in the lift interior.  It's not quite overwhelming, but it can feel like it occasionally!

Lizzie and I went on our own tour of the Legoland Windsor Hotel one evening, and tried out two of the different floors; as you can see, the Lego themes cover all parts of the decor, and Lizzie loved travelling around the different zones.

There are two main dining/eating areas, and they're situated on the ground floor (from the Legoland Park perspective) or on the second floor (of the hotel) since the hotel is built into the side of a hill.  There's a more adult-based bar area - with a conventional bar and more typical pub/bar type seating - although children are obviously still welcome, along with a family-centred dining area, where breakfast and evening meals are served.  The Lego decor is toned down in the bar area, but well and truly scaled up in the restaurant area, with large-scale models of minifigures cooking, baking, serving, mixing and so on.

Between the bar and restaurant areas, is an open space containing a play tree and a play castle, with its own Lego monster, which Lizzie and Ben both enjoyed.  In fact, only at Legoland would you hear the following conversation:

"Excuse me, can you tell me where the toilets are please?"
"Certainly sir, just behind the castle."



A word of warning on the restaurant - it's not cheap.  At £20 a head, it's a little on the pricey side, but it is all-you-can-eat for evenings.  However, breakfast (included in our room rate) was also all-you-can-eat, and is very well stocked with a wide range of food.  And the bonus of this being Legoland, is the costumed entertainers who call round from time to time to say hello - this was a real bonus for us!

Captain Birdseye (?), left, and Johnny Thunder (above) call in for breakfast on two of the days we were at the restaurant - as you can see, Lizzie was very pleased with both of them!

The hotel rooms themselves are well designed and spacious as hotel rooms go.  We had a basic room, which  meant it didn't overlook the park.  Instead, we overlooked (in the distance) Heathrow airport, and during the evenings we could see the distant lights of aircraft approaching and landing.  A word of note - the hotel is directly on the flightline.  You don't get much noise from the aircraft, but you will get to see the aircraft taking off or landing - and when they're landing, they come in lower than they take off.

















As I mentioned earlier, we visited the hotel only a few days after it had opened, and the staff were working through one or two teething issues.  For example:


*  the swimming pool and wet play area were not available throughout our stay.  Another visitor told us that they'd been offered a £20 voucher to spend in the shop (not a huge shop, but it had a range of Lego models and other items), and when we asked, we were told it would be taken off our bill.  In the end, we had a separate refund a few days later.

*  Check-in and check-out took ages - I think the staff were getting used to the system!


*  The entrance from the hotel to the theme park is conveniently located just outside the restaurant/bar area.  However, the intended access is through a full-height turnstile, which is a complete no-no if you have a pushchair.  There is a gate, locked, next to the turnstile; on the first morning we had to go and find somebody to let us into the park, on the first afternoon he was closer at hand, but by the second morning there was a new member of staff fully kitted out with ticket scanner and so on, to help us through.  Overall, this wasn't an issue, and it stands out as poor planning in an otherwise very well thought out design.



Overall, I would strongly recommend the Legoland Windsor Resort Hotel for a family.  I know I haven't discussed the theme park - that'll come as a separate review later!

Chemistry Apparatus Cartoons: The Test Tube

This follows on from yesterday's post, the beaker.  There isn't much more to say, really, except that you'll start to see the overall cartoon/pun theme develop from here onwards.  I've always enjoyed chemistry and always had a liking for puns and cartoons... the rest is obvious!  The next post will be a development from the test tube.

I've produced a short series of Chemistry cartoons, including The Test Tube, The Side-Arm Test Tube, The Delivery Tube, the beaker and The Measuring Cylinder.  I do have a 'formal' Chemistry background, and have also written some more serious articles on Chemistry, including how I transferred from Chemistry to a career in online web analytics.

Chemistry Apparatus Cartoons: The Beaker

This post is very short; in fact it'll be one of the shortest I ever produce.  However, it will also be the first in a series, and the series is 'chemistry cartoons'.  I first drew these around 10 years ago, and I've redrawn them and improved them a little since then, but they're very similar to the originals.

The first is the beaker.

More to follow shortly.

I've produced a short series of Chemistry cartoons, including The Test Tube, The Side-Arm Test Tube, The Delivery Tube, and The Measuring Cylinder.  I do have a 'formal' Chemistry background, and have also written some more serious articles on Chemistry, including how I transferred from Chemistry to a career in online web analytics.

Maths: Fibonacci Series (Multiplying Rabbits)

Consider, for a moment, a pair of adult rabbits in the wild.  Rabbits reproduce very quickly, (let's say once every month), and let's suppose that each time a pair of rabbits reproduces, it produces two young rabbits, one male and one female.  After a month, the new young pair is capable of reproducing.  What would happen to the population of pairs of rabbits over a number of years?


At the start of the first month, there's one pair of rabbits.  =1
After the first month, there's one pair of rabbits (and one young pair) =2
After the second month, there are two pairs of rabbits (the original pair, and the young ones have now matured) plus one young pair (from the original couple) =3
After the third month, there are now three adult pairs, and two young pairs (from the two adult pairs) = 5
After the fourth month, there are five adult pairs (three old ones, plus the two from the last generation), and three young pairs (from the three mature pairs last time) = 8


Finally (for this discussion), after the fifth month, there are eight adult pairs (five plus the three new pairs) and five adult pairs = 13 pairs of rabbits.


Let's look at the sequence again...
To start with, we had 1.  Then 1 again, then 2, 3, 5, 8, 13.


This sequence is known as the Fibonacci series, after the Italian gentleman who first identified it (Leonardo Fibonacci, 1170-1230).  In simple terms:  to find the next number in the sequence, add together the previous two numbers.


1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89 and so on.


Fibonacci - Mathematics


This sequence grows very quickly - as the rabbit population would - and it has some interesting properties.  Firstly, though, it doesn't graph very well on a normal graph scale...

The large values for the later terms in the sequence completely overwhelm the smaller values, so that the first part of the graph looks like a horizontal line.  A logarithmic scale on the y-axis will help show the growth in a little more detail.  The vertical y-axis now counts 1, 10, 100, 1000 etc with equal spacing.

Which shows something I suspected - we can accurately describe the Fibonacci series as logarithmic.  

Let's look at how quickly the series increases, by dividing each term by the previous one.

We can see that the growth rate fluctuates for the first few terms, but after eight terms, settles down considerably, and then reaches a value of 1.618033988749890 after 40 terms.  This number is called the Golden Ratio, and it appears in various mathematical (and non-mathematical) situations.

Borrowing from Wikipedia, the Golden Ratio can be defined as...

Rectangle

The ancient Greeks knew of a rectangle whose sides are in the ratio of the Golden Ratio.

It also occurs naturally in some of the proportions of the Five Platonic Solids (the tetrahedron, cube, octahedron, dodecahedron and icosahedron).   This so-called Golden Rectangle appears in many of the proportions of that famous ancient Greek temple, the Parthenon, and in the Acropolis in Athens. However, there's no original documentary evidence that this was deliberately designed in.  A Golden Rectangle also has visually pleasing proportions, see the larger rectangle below.  The horizontal sides are length 1, the vertical sides are lenth 1.61803...

Spiral

The Fibonnaci series can be used to produce a spiral; the title link above shows how this is done.  However, to summarise, by drawing squares with sides equal to the terms of the Fibonacci series, adjacent to each other, and by proceeding in a clockwise (or anti-clockwise) manner, it's possible to draw up a connected series of squares.  Yes, I'm borrowing from Wikipedia again:

And then draw quarter-circular arcs using the corners of the squares, so that they trace out into a spiral.  The area in red below corresponds to the area shown above.

Fibonacci in Nature

Apart from unchecked rabbit populations, the Fibonacci series shows up in a number of natural places - in flower petals, pine cones and so on.  My personal favourite is where the Fibonnaci spiral shows up in shells, and I've had this picture on the wall next to my desk for some time.  It reminds that even though numbers can get pretty ugly, they can also look remarkably beautiful.

The volume of each chamber within the shell follows the Fibonacci series, all the way out to 3,524,578.

Many other spirals also follow the Fibonacci series.  So we can see the Fibonacci series has a wide scope, from the huge to the tiny;overall, though, the Fibonacci series is as simple as 1, 1, 2, 3 :-)

Other maths articles on a similar theme:

The Fibonacci Series
Fibonacci Constants Revisited
The Collatz Conjecture

Ulam Sequences

Word 3:45 Two: Matthew 2

Matthew 2

Matthew's gospel moves very quickly from Jesus's genealogy, a few paragraphs about his birth (compared to Luke who spends two chapters there) and straight on to the visit of the Magi, then Herod's plans to find and kill Jesus.

Verses 22-23 of Matthew 1 reads, "All this took place to fulfill what the Lord had said through the prophet 'The virgin will conceive and give birth to a son, and they will call him Immanuel'(which means “God with us”)."  This is a recurring theme throughout Matthew's gospel; he constantly points to the Old Testament prophecies about the Messiah, and then shows that Jesus was fulfilling them.  The phrase, "this took place to fulfill the prophecy.." or similar, occurs once in Matthew 1 (not including the entire genealogy, which we saw last time is a great long list of fulfilled promises) and three times in Matthew 2, and that's just for starters!

In Matthew 2 we get political refugees and infant genocide.  We wouldn't normally call it that, because it's all couched safely in different words than that, but that's what it comes down to.  Joseph and Mary have to flee to Egypt with Jesus, to avoid the slaughter of all young boys that was ordered by a paranoid Herod.  

Matthew 2 is a short chapter, just 21 verses, and most of it is very well known.  It's straight-forward enough, but one question I have is why go to Egypt?  Why not forget about the whole incident, or perhaps God could have directed the wise men directly to Bethlehem instead of to King Herod?  There are parallels with Moses, who led the people out of Egypt and into the Promised Land, which could well be what Matthew is highlighting here.  

I should mention at this point that Luke's gospel doesn't have the 'flight to Egypt', but Matthew and Luke aren't contradicting each other - it's just that they're highlighting certain events.  Luke doesn't feel it's relevant to include the flight to Egypt, but Matthew does, for other reasons.  Matthew is aiming throughout his gospel to highlight how Jesus was foretold in the Old Testament, and the parallels with other Old Testament characters help him to support and highlight this point.

Other articles I've written based on Biblical principles

10 things I learned from not quite reading the Bible in a year
Advent and a Trip to London
Advent: Names and Titles
Reading Matthew 1
My reading of Matthew 2
The Parable of the 99 Sheep
Why I Like Snow (and isn't as crazy as you may think)

Puzzle: Snakes and Ladders

(also known as the Collatz conjecture, or Syracuse problem)


Courtesy of Calculator Fun and Games, which first introduced me to it, here's an interesting puzzle that is easy enough to understand, but which has developed into a far more complicated problem.  In fact, if you want to make the easy idea hard to understand, just go and read the Wikipedia entry - it is far too complicated, as much of maths on Wikipedia tends to be.


Anyway, here it is: Take a number - any number.  If it's odd, multiply by three and add one.  If it's even, divide by two.  Now take your new number and follow the same process - odd numbers multiply by three and add one, even numbers divide by two.  And so on, and so on.  

What do you find?  And, more importantly, does this always happen?


Let's try a few numbers:
35 is odd, so multiply by 3 ( = 105) and then add 1 = 106
106 is even, so divide by 2 = 53
53 is odd, so multiply by 3 (=159) and then add 1 = 160
160 is even, so divide by 2 = 80
80 is even, so divide by 2 = 40
40 is even, so divide by 2 = 20
20 is even, so divide by 2 = 10
10 is even, so divide by 2 = 5
5 is odd so multiply by 3 and add 1 = 16
16 is even, divide by 2 = 8, which is also even, divide by 2 = 4, then 2, then 1.


If (or should that be "When"?) you reach 1, then you stop.  Otherwise, you get stuck in a loop that goes 1 -- 4 -- 2 -- 1 -- 4 -- 2 etc.


The question is:  Do you always reach 1?  Is there a number out there somewhere that doesn't eventually drop down to 1?


The path length for numbers (how long it takes for a number to reach 1) is not predictable - certainly not easily, as far as I know, and so there's much research there as well.


For example, 26 follows the path 26 - 13 - 40 - 20 - 10 - 5 - 17 - 8 - 4 - 2 - 1


But 27 follows a completely different path...
27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077,9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1


...with its highest point at over 9,000!  All in all, it has 111 steps in its path to 1.

Image from Calculator Fun and Games
(original was black and white line drawing)

Here are the paths for all the numbers 1-20 (and the numbers that they include):

Image from: "Professor Stewart's Hoard of Mathematical Treasures"

There are various puzzles connected with this problem.  The main one is to prove that all paths end at 1, but that's still not been completely solved yet, and some of mathematics' greatest minds are having a go.

A good alternative, though, is to find the longest path possible for three-digit and four-digit figures.  I'm not sure if it's a puzzle, or a game, and if it's a game, then I figure it'd probably spoil it for you to know the answer before you start :-)

This was my first post on the Collatz conjecture, but I enjoyed investigating it so much that I wrote (and continue to write) a series of articles about variations on it, and you can find them in my Collatz conjecture category.  The next article in the series is Collatz Conjecture 5n+1 and after that, Collatz Conjecture 3n+3.

Puzzle: Magic Square

I'm not entirely sure if this puzzle already has a name... it probably does, but I haven't found it. I think it's probably fair to call it a magic square, since the idea is to use a set of numbers in a square to achieve the same total in the rows, columns and long diagonals.  The difference here is that the numbers are four sets of the numbers 1-4, in four different colours (white, grey, black and yellow), and there's an additional condition that no row, column or long diagonal must have a colour repeated.


To make it easier to explain, here is a set of blocks, showing the four digits 1-4 in their four colours (sixteen blocks in total).

There are a number of solutions to this puzzle, and I have no intention of calculating the number.  Instead, I'm going to look at an example solution, and discuss my thoughts on it, so that - hopefully - you'll be able to solve similar problems in the future.

I was going to insert a few line breaks here, just in case you're included to try and solve the problem without the solution.  

However, I suspect the answer is complicated enough that you won't solve it just by glancing at the answer!

Here's one solution, then:

There are a number of comments I'd like to make on this solution, but before I do, I'd like to introduce (or re-introduce, if you've seen it before) a distance that I call the knight-move.  In Chess, the knight moves by going one square forwards, backwards, or left or right, followed by two squares left, right, or backwards or forwards (at 90^o to the original direction) .  Again, it's easier to show with a diagram, so here goes:

This motif shows up a number of times in the magic square puzzle here, and in many other puzzles of the type, "Arrange the numbers so that such-and-such don't appear in the same row or column."  Let's look at the solution again; firstly, here are all the 4s.

Can you see how the 4s are all connected by a knight-move, starting from the four in the top corner?  The sequence grey-yellow-white-black is a series of three knight-moves.

The same applies for any of the other numbers, for example, the 2s start from the bottom right.  The whole solution has rotational symmetry - if you imagine moving the grid around by a quarter turn, then you find the same solution for a different number (1, 4 , 2, 3 in this example).


The same also applies for the coloured numbers - in the next diagram I've highlighted the white numbers.  Starting in the lower right corner with 2, the white numbers are all connected by knight-moves (one across and two up, or two across and one down, etc).

Notice here that one knight move from the white 2 gives the white sequence (shown above), while the other knight move from that 2 gives the sequence for all the other 2s.


So, whenever you encounter any puzzle of the form, "Put the objects into the grid so that each row and column only contains one of each type of object" - whether it's numbers, letters, or shapes, remember the knight-move as a short cut towards the solution!