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Number 14: Wacky stomachy and wise teens

An ancient puzzle, a dummy spit on the golf course and no fours on the floor. We’ve packed a fortnight of fun into number 014 and you're invited along for the ride!

Wacky stomachy


The ancient puzzle known as the ‘stomachion’ contains 14 pieces which can be arranged in a square. Though around since at least the time of Archimedes (287–212 BC), it wasn’t until 2003 that Bill Cutler used a computer to show that this can be done an amazing 17,152 ways. If you remove solutions that are rotations and reflections of each other, Cutler found 536 unique solutions.


Unwelcome clubs


When playing PGA golf, you can carry no more than 14 clubs in your bag. For most amateur hackers like me, having more than about 8 clubs tends to freak us out, but there have been occasions where professional golfers have been penalised for accidentally having too many clubs in their bag.


At the 2001 British Open, the great Welsh golfer Ian Woosnam was in a potentially winning position on the final day when his caddie uttered the immortal words, ‘You’re going to go ballistic ... we’ve got two drivers in the bag’. This is because Woosnam had been warming up with two different drivers but when he chose which one he would use for the day, his caddie accidentally left both in the bag.


Woosnam immediately realised that he would be penalised 2 strokes for carrying 15 clubs. In a moment now famous in the history of golf tantrums he threw his extra driver into the bushes!


No 4s on the floor!


As we already know from number 004, Chinese culture sees 4 as unlucky. It’s not uncommon in hotel or casino lifts for there to be no level 13 or 14. And as the photo here shows, no 24 or 34 either!


In fact in 2015 the city of Vancouver passed a rule that all new buildings must contain all floor numbers because of the confusion missing floors can cause emergency services.


“We’re back to basic math at the city,” Pat Ryan, the chief building officer said at the time.



(More) fascinating facts about 14!



Wise words


“When I was a boy of 14, my father was so ignorant I could hardly stand to have the old man around. But when I got to be 21, I was astonished at how much the old man had learned in seven years.” Mark Twain



+ve or -ve solution?


By selecting one of + or – in front of each number, there are 14 solutions to 1 2 3 4 5 6 7 8 = 0. Eg. + 1 + 2 + 3 + 4 – 5 – 6 – 7 + 8 = 0. Can you or your kid find them all?





Passports please!


China and Russia both border an incredible 14 countries. As well as a 4,209 km common border (the 6th longest border in the world), they also both border Kazakhstan and North Korea.




Cool chemistry facts


Silicon


An atom of silicon contains 14 electrons, protons and neutrons and as such it is the 14th element on the periodic table. And here is an amazing fact about silicon and something I never would have thought unless I’d read it...


Silicon is the second most abundant element in the Earth’s crust making up about 27.7% of the crust. Between it and oxygen it makes up about ¾ of the weight of the Earth’s outer layer!


But you don’t ever stub your toe on a chunk of pure silicon. You’ll find it occurs chiefly combining with oxygen to give us sand, quartz and related minerals and gems like opals (which also involve water).


The dating game


Carbon is an element crucial to life. On Earth, carbon occurs in 3 natural forms (or isotopes). All 3 of these have 6 protons in their nucleus, but the nucleus of Carbon-12 has 6 neutrons, Carbon-13 has 7 and Carbon-14 has 8.


Carbon-12 is the natural form of carbon and as such makes up approximately 99% of the carbon on Earth. Carbon-13 makes up about 1%.


That doesn’t leave much room for Carbon-14, in fact only 0.0000000001% or 1 part per trillion of all carbon on Earth is Carbon-14.


But crucially, Carbon-14 is radioactive, with a half-life of about 5730 years. Measuring how much of it is in stuff is the cornerstone of ‘carbon dating’, central to working out the age of fossils and so on, giving us a fascinating look back into history.


Catalan numbers


There are 5 ways of dividing a pentagon (a 5-sided figure) into 3 triangles:

The formula for the number of ways you can divide a regular polygon with (n + 2) sides into n triangles is given by the Catalan equation:




... which I know is enough to make you almost lose your lunch, but trust me isn’t that bad.


Remember that 3! = 3 x 2 x 1 = 6, that 4! = 4 x 3 x 2 x 1 = 24 and so on.


So to divide a pentagon into 3 triangles, let n = 3 and the Catalan equation simply becomes:




So some simple maths give us:


C(3) = 5


So there are 5 ways to divide a pentagon into 3 triangles.


If you’re really feeling game, convince yourself that C(4) = 14 and that there are 14 ways to divide a hexagon into 4 triangles ... here are 2:








That's it from me for now. Why not browse my other newsletters below?!


Yours in numbers,

Adam

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