Funbers 31, 32 and 33
The fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…
31 — Thirty-one
Hands up if you like ice cream? And your favourite brand? I’m not sure I could pick a favourite myself, but Baskin-Robbins is certainly up there. They have a total of 31 flavours of ice cream which means the name of their shops in Japan literally translates as ’31 Ice Cream’. In theory a great idea, but what if they discover a magical new thirty-second flavour…
Aside from frozen goods, thirty-one is also the number of teams in the National Hockey League, with 24 coming from the US and 7 from their Northern neighbours Canada. Each season, the teams battle it out to win the Stanley Cup — the oldest trophy to be awarded in professional sport in North America, and also the one with the infamously large base (see below). Originally, key members of the winning team were engraved on the base, which means its grown a fair few inches over the past 126 years. However, these days the oldest band is removed and replaced with a new one to prevent the trophy from getting any bigger. Less fun no doubt, but perhaps sensible given its already considerable size…
Thirty-one is also a Mersenne Prime — the third such one in fact. A Mersenne Prime is a prime number that can be expressed as exactly one less than a power of two: 2^n — 1 for some positive whole number n. To get 31, we take n=5: 2⁵ = 2 x 2 x 2 x 2 x 2 = 32 minus 1 gives 31. A perhaps surprisingly large (and possibly infinite) amount of prime numbers take this form, with the current largest known prime number also being a Mersenne Prime: 2⁸²⁵⁸⁹⁹³³–1 = a number with 24,862,048 digits, aka too many for me to write out here!
32 — Thirty-two
Sticking with maths, thirty-two has the very nice property that it can be written as 1 to the power 1 plus 2 to the power 2 plus three to the power three, or in its neatest form: 1¹ + 2² + 3³ = 32. Here’s a challenge for you: can you work out the next largest number that follows the same pattern?
32 can also be written as 2⁴ + 4² = 32 which makes it a Leyland Number. Any number that can be written using two other numbers x and y, in the pattern x to the power y plus y to the power x, is classified as a Leyland Number. Here, we take x = 2 and y = 4 to get: 2⁴ = 2 x 2 x 2 x 2 = 16, plus 4² = 4 x 4 = 16, giving a total of 16 + 16 = 32. Other Leyland Numbers include: 8, 17, 54, 57 and 100 — I’ll leave it to you to figure out the specific values of x and y needed to satisfy the formula x^y + y^x = Leyland Number for each of the cases above.
Outside of the mathematical world, thirty-two is the number of completed piano sonatas by Ludwig van Beethoven; the number of black (or white) squares, and total number of pieces on a chessboard; the number of teeth generally found in an adult human; and the number of described physical characteristics of the historical Buddha, according to the text of the Pāli Canon in the Theravada Buddhist tradition. It’s a pretty long list, but I think it is best enjoyed in its entirety, so here you go:
1. Level feet
2. Thousand-spoked wheel sign on feet
3. Long, slender fingers
4. Pliant hands and feet
5. Toes and fingers finely webbed
6. Full-sized heels
7. Arched insteps
8. Thighs like a royal stag
9. Hands reaching below the knees
10. Well-retracted male organ
11. Height and stretch of arms equal
12. Every hair-root dark coloured
13. Body hair graceful and curly
14. Golden-hued body
15. Ten-foot aura around him
16. Soft, smooth skin
17. Soles, palms, shoulders, and crown of head well-rounded
18. Area below armpits well-filled
19. Lion-shaped body
20. Body erect and upright
21. Full, round shoulders
22. Forty teeth
23. Teeth white, even, and close
24. Four canine teeth pure white
25. Jaw like a lion
26. Saliva that improves the taste of all food
27. Tongue long and broad
28. Voice deep and resonant
29. Eyes deep blue
30. Eyelashes like a royal bull
31. White ūrṇā curl that emits light between eyebrows
32. Fleshy protuberance on the crown of the head
33 — Thirty-three
Let’s start with the bad. Thirty-three is one of the symbols of the Ku Klux Klan, with K being the 11th letter of the alphabet and 3 x 11 or 3 K’s giving 33. It is also believed to be the age of Jesus when he was crucified by the Romans.
On a more positive note, 33 is the longest winning streak ever recorded in NBA history, which was achieved by the Los Angeles Lakers in the 1971–72 season. We also find 33 vertebrae in a normal human spine when the bones that form the coccyx (the tail-like part at the bottom) are counted individually.
Now I don’t say this often — mainly because I think I’m supposed to be impartial when writing these — but this next fun fact is one of my all-time favourites. Long playing records, or LPs as they are more commonly known, are referred to as 33’s in the record industry, because they rotate 33 and a third times per minute when playing on a gramophone. So, next time you see a record player you know what to do…
Author
The Funbers series is written and presented by Dr Tom Crawford and is broadcast weekly on BBC radio. For more maths fun check out Tom’s website tomrocksmaths.com and follow him on Twitter, Facebook, Instagram and YouTube @tomrocksmaths.
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