Numbers 1,2,3,4,5 from 1 to 200

Since pure and applied Maths are constantly expanding, it seems only fair that I should expand my tiny contribution to the field of puzzle solving.  My recent Maths posts have looked at the puzzle of making the numbers from 1 to 200 using only the four digits 1, 2, 3 and 4 and I've been very grateful for the support of the Maths community in solving this puzzle.  (1-100), (101-150), (151-200)

Extending this then, I set my mind to seeing if this can be done with the digits 1-5.  In some ways it's easier, in other ways it is more tricky. I've managed to solve for 1-200 (single-handedly, which suggests it's an easier task).  There is less need to employ factorials, and if I recall correctly, I've completed my solution without any decimals. 

Note
It is of course possible to take the four-number solution for (n-5) and attach a +5 at the end of the expression.  Or alternatively, any number between 121 and 320 can be achieved easily by adding 5! to the four-number solution. I have avoided these short-cuts (with one exception where I could not find an alternative - 178).

Here is part 1, going from 1 to 100:

1 = 1 * ((5+2)/(4+3))
2 = 1 + ((5+2)/(4+3))
3 = 3 * ((1+5)/(4+2))
4 = 4 * (1*5)/(2+3))
5 = 5 * ((4+1)/(2+3))
6 = (14*3) / (2+5)
7 = 35 / ((4+2) - 1)
8 = 32 / ((5+4) -1)
9 = (34+2) / (5-1)
10 = (1 + 24 + 5) / 3
11 = (15 - 4) * (3-2)
12 = 45/3 - (1+2)
13 = (4^2 - 5) + (3-1)
14 = (32/4) + 5 + 1
15 = (51-32) - 4
16 = (52 - 4) / (3 * 1)
17 = 25 - (4 + 3 + 1)
18 = 54/3 * (2-1)
19 = (54 + 1 + 2) / 3
20 = (42/3) + 5 + 1
21 = (54/3) + 1 + 2
22 = 32 - (1 + 5 + 4)
23 = (45 - 23) + 1
24 = 54/2 - (1*3)
25 = (52 + 4) -31
26 = (14 * (3/2)) + 5
27 = (53 -1) / (4-2)
28 = (54+2) / (3-1)
29 = (35-(4+2)) * 1
30 = (45 * 2)/(1 * 3)
31 = 5^2 + 4 + (2*1)
32 = (51+4) - 23
33 = 24 + 1+ 5 + 3
34 = 2^5 + 1 + (4-3)
35 = (152/4) -3
36 = (54+3) -21
37 = (5+1)^2 + (4-3)
38 = (132/4) + 5
39 = 1* 4^3 - 5^2
40 = 5! / ((12+3) / (1+4))
41 = (52+3) - 14
42 = (4*5*2) + (3-1)
43 = (125+4) /3
44 = (45*1) + (3-2)
45 = (54 - 3^2) * 1
46 = ((5*4) + (3*1)) * 2
47 = (35+14) -2
48 = (45+3) * (2-1)
49 = ((5+4+1)-3)^2
50 = (25*4)/(3-1)
51 = 34 + 15 + 2
52 = (4*5*1)+32
53 = (34*2) - 15
54 = 3^2 + 45 * 1
55 = (15*4) - (3+2)
56 = (2*4) * (5 + (3-1))
57 = (13*5) - (2*4)
58 = (25+4) * (3-1)
59 = (3*4*5) - (2-1)
60 = 1 + 24 + 35
61 = (1* 4^3) - (5-2)
62 = 13*4 + (2*5)
63 = (34 * 2) - (5*1)
64 = 3^4 - (15 + 2)
65 = (54 + 13) -2
66 = (35 * 2) - (4 *1)
67 = (24*3) - (5*1)
68 = (42+31) - 5
69 = 132 - 54
70 = (25 * 3) - (1*4)
71 = (43 * 2) -15
72 = (34*2) + (5-1)
73 = 3^4 - (5+2+1)
74 = 4^3 + (1 + 5 + 2)
75 = (35*2) + 1 + 4
76 = ((35 + 4) -1) * 2
77 = (3+4) * ((5*2) +1)
78 = (25 * 3) + (4-1)
79 = ((5^2) * 3))+(4*1)
80 = (2*41) - (5-3)
81 = (5+4) * 3^2 * 1
82 = 134 - 52
83 = (4^2 * 5) + (3*1)
84 = (35 * 2) + 14
85 = (5! - 32) - (4-1)
86 = (21 * 4) + (5-3)
87 = 54 + 31 + 2
88 = (45 * 2) - (3-1)
89 = (13 * 5) + 24
90 = (41 + 52) - 3
91 = 13 * ((5+4)-2)
92 = (45 * 2) + (3-1)
93 = (14 * 5) + 23
94 = (45 * 2) + 1 + 3
95 = (51 * 2) - (3+4)
96 = (45 + 3) * 1 * 2
97 = (25 * 4) - (3 * 1)
98 = (41 * 3) - 25
99 = (21 * 4) + (3 * 5)
100 = ((53 - 4) + 1) * 2

Next time: 101 - 200. 

Numbers 1,2,3,4 from 151 to 200

After my previous posts on using the digits 1,2,3,4 and mathematical operators (which, by the way, have become increasingly creative and powerful) to create the numbers 1-50, then 51-100 and 101 to 150, I'd like to present a team effort on the numbers from 151 to 200.  I didn't think it was possible.  In fact, I very much doubt that the authors of the maths textbook that posed the original idea thought it would be possible.  Nonetheless, here it is:  use the digits 1,2,3,4 and any mathematical operators you care to name to produce the totals from 151 to 200.

Credit to Denis from the freemathhelp forum for his work on this, providing the vast majority of the results and taking the problem way beyond its original scope.  Major credit also to Skipjack for providing the solutions marked with an asterisk.

To clarify, r(.1) = repeating decimal.

151: (4! + 3!) / .2 + 1

152: (1 + 4)! + 32

153: 34 / 2 / r(.1)

154: 2^4 / .1 - 3!

155: 31 * 2 / .4

156:4! * 3! + 12

157: 314 / 2

158: 3!! * .2 + 14

159: 3!! / 4 - 21

160: 32 * (1 + 4)

161: 3^4 * 2 - 1

162: 3^4 * 2 * 1

163: 3^4 * 2 + 1

164: (3! - 2) * 41

165: 4! + 3! + 21

*166: 4! * (3! + 1) - 2

167: 13^2 - SQRT(4)

168: 14 * 3! * 2

169: 13^(4 - 2)

170: 34 / .2 * 1

171: 13^2 + SQRT(4)

172 = .1^(-2) + 3 * 4!

173: 13^2 + 4

*174: 3! * (4! + 1 / .2)

175: 3!! / 4 - 1 / .2

*176: 4! / .1 - 2^3!

177: 3!! / 4 - 1 - 2

178: 3!! / 4 - 1 * 2

179: 3!! / 4 + 1 - 2

180: 3!! / 4 * (2 - 1)

181: 3!! / 4 - 1 + 2

182: 3!! / 4 + 1 * 2

183: 3!! / 4 + 1 + 2

184: 3!! * .2 + 4 / .1

185: 3!! * .2 + 41

186: (2 + 4) * 31

*187: (4! - 3) / r(.1) - 2

188 = (.1^(-2) - 3!) * SQRT(4)

189: 213 - 4!

190: 14^2 - 3!

191: 4! * 2^3 - 1

192: 3!! / 4 + 12

193: 14^2 - 3

194: 4 / .1 / .2 - 3!

195 = (4! - 2) / r(.1) - 3

*196: 4 * (3! + 1)^2

197: 4 / .1 / .2 - 3

198 = (3! * 4 - 2) / r(.1)

199: 14^2 + 3

200: (2 + 3) * 4 / .1

What happens if your test wins?

Online testing can be difficult, and getting a winner can be especially hard.  But what happens when your test wins?  Do you have a plan in place?

When a test loses, we tend to analyse the results more carefully than when it wins - to quote Wikipedia's entry on loss aversion and prospect theory, "Losses hurt more than gains feel good."  And if a test loses, there's no immediate action required (apart from switching the test off).  But if it wins, then there'll be the follow-up questions "Why did it win?" (occasionally) and "Can we implement it?" (almost 100% of the time).

The easiest way to implement a test winner is to use your testing tool to simply transfer 100% of traffic to the winning recipe, and a number of web optimisation professionals that I've spoken to use this process.  It's straightforward, However, there are a number of potential drawbacks to this, which you may need to consider:

-If you're using the testing tool to support a winning implementation, you can't use that testing code for further tests.
-In order to display the winner, you'll be relying on a server call to and from the testing tool server (which may slow down page load time), 
-If your contract with your test provider means that you're billed on server calls, you'll be incurring a fee each time the page loads (probably not significant compared to your total revenue and income, but something you may need to consider).

If these are significant issues for you to consider - and to be fair, they may not be important for you - then you'll need to have another route to getting your win implemented.  A good personal network within your company will certainly  help at this stage, as will some understanding of how your site is put together.  You don't need to be completely conversant in HTML, AJAX and JavaScript (although a basic understanding will certainly help you make valid contributions to discussions around implementation - and testing generally) but being able to see how your test win could be implemented will certainly help.

Here are some potentially easy implementations:

Swapping images - if you can show that lifestyle images work better than product-on-a-white-background - is easy enough, and can be implemented in an ongoing way.

Headlines - and text changes - should be straightforward, for hardcoded sites (who uses them?) and those that pull in content from a server-side include.
I know I've said this before (so I apologise, slightly) but CTAs are a great opportunity for implementable test wins.

Making changes or additions that can be incorporated into a template change and rolled out across the site - providing your test win should be implemented globally - is doable.

More complex implementations include redesigning pages - moving content around may be doable (again, this depends on the page template, so beware).

However, adding in new snippets of code on specific pages or totally redesigning a page; creating exceptions for specific pages is trickier, and is likely to cause your HTML/JS development team a headache.  

Don't forget: apart from avoiding negative changes to your site, and informing future design,  the return on investment of your testing program is only going to come from implemented winners.  If implementing your winner is going to take your development team three months to code, then that resource cost will have to be weighed against the revenue and conversion lifts from the implementation.  There's nothing wrong with so-called "simple" tests - you can build momentum that way - and when you start achieving wins, you can scale up and start asking for more development resource. 

Similar posts I've written about online testing

Getting an online testing program off the ground
Building Momentum in Online testing
How many of your tests win?

How long should I run my test for?
 

"A/B and MVT doesn't work"

A few months ago, I wrote about my experience of how modern power-tools just don't work, and how my power-drill wasn't working as well as other people said it would.  Well, today, I've just read that A/B and multivariate testing does not work on e-Commerce sites.  And I think it's true.  After all, I read it online, so it must be true.  And it matches with another recent experience I had:  it seems my car is broken.

I've had my car for a number of years - it's a very nice car and I was fortunate enough to have it from new.  It seems to drive well, but I've found that there are a number of fundamental issues with it.

The speedometer doesn't work.  The speed readout (both digital and analogue) agree with each other to about 1%, but the maximum speed on the speedo is 150 mph, and I've never managed to achieve those speeds. I took it for a drive recently, and even though my maximum speed was 60 mph, which I achieved for a short while, it still took me 30 mins to travel 20 miles.  No - the speedometer is just plain useless.

The miles per gallon calculation on the dashboard display is inaccurate, and certainly doesn't match the driver's guide (yes, I read the driver's guide).  It keeps changing all the time - what's that all about?  Even the 'average' fuel efficiency figure changes.  Seriously?  Another important part of my car is not working properly.  The dealer says that the figures are based on "average use" (whatever that is), and over a long period of time it will average out, but I'm not prepared to wait that long.  I want to see my driving data match the actual data all the time.

Wing mirror showing rear view.

The rear-view- and wing-mirrors only show me where I've just been, and - worse still - the image is reversed (transposed left to right, horizontally).  Honestly, just how am I supposed to make sense of the image - or see where I'm going - by looking in them?

I have my own satnav - it's a mid-range TomTom model, so it's good and reliable - but when I use it in my car, the satnav predicted arrival time is wrong.  Worse still, the satnav (which has full maps of Europe) won't integrate with the car's engine and drive it for me, so I am stuck with still having to actually drive the car myself.  And did I mention that the speed readout on the satnav doesn't match the car's speedometer?

I have driven the car in heavy traffic and along long stretches of motorways; it's covered country lanes and suburban housing estates - but it's only occasionally performed as well as it's supposed to in the manual, and it only rarely displays MPG figures that match my own forecasts and predictions.

To be honest, the only things that really work as I expect them to are the odometer (mileometer) and the clock.

I've tried monitoring engine temperature (the engine is cold when it starts in winter and is generally warmer in summer); oil pressure (unaffected); brake pad usage (it goes up when I travel through busier streets) and so on, but none of these metrics have been particularly useful at helping me drive better, faster or further.

I've attempted to forecast my future mileage, fuel efficiency and average speed based on the distances I covered yesterday, last week and last month.  It's almost impossible - it seems that it varies day by day.  Having said that, we went on a family holiday round North Wales last August, and I know we're not going this year, so I can expect a decrease in my average mileage for this year.  And my fuel efficiency will be lower because I won't be driving as many of the long, steady dual-carriageway runs that I did last year.  But these are just estimates really, based only on actual events that happened last year but won't happen this year.

My car is on a three-year lease, and the lease expires next summer.  I will probably swap it for a different car, but I'd like to know how that car's fuel efficiency and speed performance will compare with my current one.  Not just what the rear view mirrors look like, or the maximum speed on the speedometer, or even what the driver's manual says. 

Perhaps I should continue to drive as I usually do for the next 6-12 months, and ask someone to drive around, following me, in my potential purchase.  Then, next summer, maybe we can compare their actual performances and choose between keeping my car or swapping it?  Who knows?

I've used car performance as an analogy to online testing before:
How long to run an A/B test for? (2013)
Who holds the steering wheel? (2011)

Numbers 1,2,3,4 from 100 to 150

Following on from last month's post about achieving the numbers from 1 to 50 (and then from 1 to 100) using just the digits 1,2,3,4 and the maths operators + - / *  and powers and factorials, I've gone a step further (and possibly a step too far) - from 101 to 150.  This is proving far more difficult - as you would expect - and so far I've only managed around 30 of the 50.  If the numbers below are blank, it's because I haven't solved them yet :-)

Major thanks to Denis and to lookagain from the Free Math Help Forum for their many solutions and for helping me fill the gaps that I had.  Denis's solutions are in purple, lookagain's are indicated in blue.  You'll see that in two cases, we've had to use the FLOOR function (i.e. the result of an operation is rounded down to the nearest integer) - we're trying to avoid using this where possible.  If you have any better solutions, please let me know!

101 = (4! / .3) + 21

102 = 3! * (21-4)

103 = 4√.1∗.2 + 3

104 = (4! + 2) * (3+1)

105 = 21 * [3 + SQRT(4)]

106 = (3+2)! - 14

107 = 4!.2−13

108 = 4 * (3 ^ (2 + 1))

109 =  4!−1.2−3!

110 = (31 + 4!) * 2

111= (1+4)! - 3^2

112 = (1+3!) *4^2

113 = (4! / .2) -1 - 3!

114 = (1+4)! – (3 * 2)

115 = (1+4)! – (3 + 2)

116 = (3+2)! – (1 * 4)

117 = (3+2)! – (4 - 1)

118 = 124 - 3!

119 = (4+1)! – (3 - 2)

120 = (4+1)! * (3 - 2)

121 = (4+1)! + (3 - 2)

122 = (3! * 21) – 4

123 = (42 – 1) * 3

124 = (3+2)! + (1 * 4)

125 = (1+4)! + 3 + 2

126 = 42 * 3 * 1

127 = (42 * 3) + 1

128 = 1 *(2 ^ (3+4))

129 = (42 + 1) * 3

130 = (3! * 21) + 4

131 = 1+4!.2+3!

132 = (31 + 2) * 4

133 = 4! / .2  + 13

134 = (3+2)! + 14

135 = (21+4!) * 3

136 = 132 + 4

137 = FLOOR (412/3)

138 = (24 - 1) * 3!

139 = 142 - 3  

140 = (1 + 3 + 4!) / .2

141 = (3! * 4!) – (2 + 1)

142 = (3! * 4!) – (2 * 1)

143 = (3! * 4!)  – (2 - 1)

144 = (3 * 4) ^ (2 * 1) = (3 * 2)! / (4 + 1)

145 = (13^2) - 4!

146 = (3! * 4!) + (2 * 1)

147 = (3! * 4!) + 2 + 1

148 = 142 + 3!

149 = (4! + 3!) /0.2  - 1

150 = 3! * (21 + 4)

Online Optimisation is a Game of Chess

It occurred to me recently that there are some similarities between playing a game of Chess and optimising a website through testing (apart from the considerable differences between them).

 Many years ago, when I started this blog, I envisaged it as a place where I would type up my chess games, with commentary, lessons and points for improvement.  A quick glance through my archive of blog posts will quickly show that the blog really hasn't matched its original plan.  It evolved and changed, in particular in 2011, when I shared my first few posts about web analytics and I realised that I could attract significantly more readers by blogging and sharing about web analytics than I have ever managed with Chess.  I figure that Chess is a much more mature subject, with many more people who are considerably more experienced than me; whereas web analytics (and especially my main area of interest, testing) is a much younger field, and there's scope for sharing ideas and experiences which are still novel and interesting.  However, there are some similarities between the two - here are a few thoughts.


Strategies and Tactics

Black prepares a tactic.

Plans in Chess can be broadly separated into strategies (long-term aims) and tactics (short term two-or-three move plans).  The long-term aim is to checkmate your opponent's king, and throughout the game that will become the more prominent goal.  In the short term, as you progress through the opening moves, you'll identify potential opportunities to capture your opponent's pieces, to put your pieces on good squares and to restrict your opponent's chances of beating you.  Some of these are short term, some are long term.  For example, it may be possible to win one of your opponent's bishops with a cunning trap (if your opponent is not vigilant).  This will make it easier to achieve your long-term goal of winning the game by checkmating your opponent.

Testing offers the same range of opportunities:  are you looking for quick wins (who isn't?) or are you planning to redesign an entire page, or even an entire site?  Will you be implementing wins as soon as you have confirmed results, or are you going to iterate and try to do even better?  Are you compiling wins to launch in one big bang, or are you testing, implementing and then repeating?  How far ahead are you planning?  Neither approach is necessarily better, as long as you're planning, and everybody is agreed on the plan!


Aims and Goals

White threatens checkmate.

As I've just mentioned, in Chess there's a clear goal:  checkmate your opponent's king, by threatening to capture his king and leaving him with no way to escape.  The aim for your online testing program may not be so clear cut, and if it isn't, then it might be time to find one single aim for it.  You might call it the mission statement for your optimisation program, but whatever you call it, it's important that everybody who's involved in your program understands the purpose of the testing team.  The same applies to each test, as I've mentioned before - each test should have a clear aim, that everybody understands and that can be measured in some clearly-defined way.

Values and KPIs

Each piece in Chess has a certain nominal value; the values aren't precise, but they provide a meaningful comparison of the strength and ability of each piece.  For example, the rook is worth five pawns, the knight and bishop are worth three pawns each, and the queen is worth nine.  This enables players to quickly evaluate a position in a game and say which player is winning, or if the position is roughly equal.  It's slightly more complicated than that, as you have to take into consideration the position of the pieces and so on, but a quick comparison of the total material value that each player has will give a good idea of who's winning.

Rooks are worth five pawns; bishops are worth three pawns and queens are worth nine.

This also means that it's possible to determine if a plan or a strategy is likely to win and is worth pursuing.  It may be possible to trap your opponent's rook (worth five pawns), but if doing so will mean losing two knights (each worth three pawns) and a pawn, then the trap is not really beneficial to you.  If, on the other hand, you could trap your opponent's king (winning the game) at the cost of two rooks and a knight, then that's definitely worth doing.
 
The key performance indicator for a game of Chess is your opponent's king, and if you can measure how close you are to capturing (or checkmating) your opponent's king, then you can see how close you are to winning the game.  You also need to keep your own king safe, but that's where the analogy breaks down :-)

White wins despite less material.

In online testing, your plan, strategy and tests all need to have KPIs.  Once you've established your long-term aim, you can set KPIs against each test which are connected to achieving the long-term aim.  If you want to improve the return on investment (ROI) of your online marketing, you could look at the landing page... improve the bounce rate and the exit rate, and encourage more people to move further into your site and view your products.  Alternatively, you could look at improving conversion of visitors from cart (basket) to checkout.  Or perhaps the flow of visitors through your checkout process.  Providing you can tie each of your tests and your tactics to the overall strategy: "Improve ROI for online marketing" then you can measure whether or not it's succeeding.

Classifying your KPIs in order of importance is also important - as we saw in Chess, if you can win your opponent's pieces but lose several of yours in the process, then it's probably not a good idea.  In testing, what would you do if your test recipe had a worse bounce rate but higher overall conversion (a situation that's not impossible)?  Which is the more important metric - conversion, or bounce rate?  Would your answer be the same if it was improved conversion but lower revenue (people not spending as much per order)?  Are you going to capture your opponent's knight but lose your queen?

Win, lose or draw?

Queen takes King: checkmate!

In Chess, there are clear rules that determine the outcome of a game.  Either one player wins (so the other loses), or it's a draw, and there are various ways of drawing:  including by agreement (both players decide neither can win); by stalemate (one player cannot make any legal moves) or a drawn position where it's clear that neither player has enough material to checkmate the other.


I hate losing at Chess.  However, the truth be told, I'm not much above average as a Chess player, and I'm the weakest player at my club (this has not deterred me, and I still play for fun).  This means that I get plenty of chances to analyse my losses, and see where I could improve.  Do I make the same mistakes in future games?  Not usually, no.  

However, I'm not satisfied to stay as the weakest player in my club - I just see this as an opportunity to do some giant-slaying in my future matches.  I read books, I visit Chess websites, I practice against other people and against computers, but I especially review my own games.  Occasionally, I win.  And do I analyse my winning games?  Absolutely - I may have already seen during the game that my opponent missed a chance to beat me, but did I also miss a chance to win more easily?

In online optimisation, the rules for calling a test a win, lose or draw are still up for debate, and they vary between companies.  And so they should.  For example, how long should you run your test? Each company will have its own testing program with its own tactics and strategies, and its own requirements.  Do you want to have 99.9% confidence that a test will win, or do you want some directional test data to support something you already believed based on other data sources?  How quickly do you want to run the next test, or implement the winner?  Providing that the rules for calling the win, lose or draw are agreed in advance, I might even suggest that they could vary between tests. This is, of course, totally different from Chess, where the centuries-old rules of the game clearly state the requirements for a win or a draw.  Otherwise though, I think it's fair to say that KPIs, metrics and strategy have their approximate equivalents in pieces, pawns and plans - and that thinking and planning are definitely the way forward!

Chess cartoons taken from the 1971 printing of  Chess for Children, originally published 1960.

Mathematical Film Reviews

Here are some simple film reviews, expressed in mathematical form.  If you've seen some of the older films (or read the books), then you won't need to watch the newer ones (or perhaps they'll help you decide if you'd like to watch them).

Equilibrium = Fahrenheit 451 + 1984 + The Matrix

After Earth = Oblivion + Will Smith's son

Noah = Transformers + Merlin + Titanic -Bible

Live Die Repeat = Mission Impossible + Groundhog Day + 12:01 + Starship Troopers

White House Down = Olympus has Fallen

Earth to Echo = ET + Close Encounters + Batteries Not Included

Lucy = Limitless + Scarlett Johansson

The Philadelphia Experiment = Quantum Leap + Titanic + Time Tunnel

Looper = Back to the Future + Die Hard

X-Men: Days of Future Past = Back to the Future + The Incredibles

Guardians of the Galaxy = The Avengers Assemble + Star Wars IV

I'm not saying that all the films in Hollywood are derivative (in fact there are some very original films out there), I'm just pointing out some recent similarities I've found.  To be honest, many of the films I've mentioned here are actually favourites of mine.

On the subject of very original films, I'd like to share a brief word about 2001 A Space Odyssey.  It's widely regarded as a genre-defining ground-breaking film, so you might be surprised to learn that even though I'm a sci-fi fan, I didn't watch it until 2015 (even though it was released in 1968, years before I was born).

I don't know why I hadn't watched it until now.  Now, I wish I hadn't bothered.

For example, if you just want to watch a computer play chess, then watch Kasparov and the Machine.

If you like model spaceships and spacecraft, go to a hobby modeller shop
If you like actual spacecraft, watch the footage of the Sputnik launch and the early Apollo missions.
If you like listening to the Blue Danube Waltz, buy it on CD (or tape, or even vinyl).

If you like a murder mystery, go and watch (or read) Agatha Christie or Arthur Conan Doyle
If you like stories with a bizarre ending, watch The Italian Job or Planet of the Apes
If you like long drawn-out stories, watch Les Miserables (released 1925, at 5hr 59 mins), or the 1927 film Napoleon (at 5hr 30 mins).

All better in comparison, and all better for watching.  2001 A Space Odyssey's only claim to fame is that it did a lot of things first.  It's just a shame that it made so many mistakes at the same time, and while doing so many things first, it forgot about the basics like story-telling, pace, narrative, dialogue and just having things make sense.