Are you able to resolve it? The world’s most fascinating quantity – revealed! | Arithmetic

Earlier than we get to as we speak’s puzzles, I’d wish to introduce probably the most fascinating quantity within the universe.

108

Readers of Asian heritage will nod with familiarity. The quantity has profound significance in Hinduism, Jainism, Sikhism, Buddhism and Chinese language tradition. It’s the variety of beads on a rosary, the variety of solar salutations carried out in a yoga ceremony, the variety of Buddhas to be carved on a walnut for good luck, and the cellphone variety of the Indian Emergency Ambulance service.

Mathematically, 108 can be a famous person, a reality I solely found lately in a brand new e book by the previous Principal Chief Engineer of Indian Railways, Shyam Sunder Gupta. For instance:

108 is 1¹ x 2² x 3³ , the product of the primary three numbers raised to themselves.

108 is the smallest quantity whose divisors when taken collectively include each digit a minimum of as soon as. (The divisors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108)

108 is the biggest identified quantity n such that 2ⁿ doesn’t include a 9.

(2¹⁰⁸ = 324518553658426726783156020576256)

108 is the interior angle (in levels) of a daily pentagon

108 is the variety of free heptominoes (the Tetris-like shapes constructed from seven linked squares.)

108 is the variety of playing cards in a UNO deck.

I’ve solely scratched the floor. Gupta’s e book, Exploring the Great thing about Fascinating Numbers, has ten pages of details about 108, ending with the remark that ‘1’ stands for fact, ‘0’ for vacancy and ‘8’ is the infinity image rotated by 90 levels. “Thus the sacred quantity 108 tells us that we’re without delay one thing, nothing and every part.” The one different numbers that Gupta devotes a complete chapter to are pi, 13, 666 and 153 (presumably the second most fascinating quantity within the universe).

It could possibly be the case that the non secular significance of 108 led Asian mathematicians to catalogue fascinating properties about it. Or it could possibly be that 108 actually is a very fascinating quantity – it’s not too small, not too massive, and extremely divisible – which helped it achieve non secular significance within the first place. How good that numerologists and quantity theorists have one thing to agree about for as soon as!

Right this moment’s puzzles are about numbers with fascinating properties.

1. Sensible billions

You have got ten playing cards. On every of the playing cards is among the digits 0 to 9. Whenever you prepare the playing cards in a line you get a quantity between 0123456789 and 987654321

i) What number of of those numbers are divisible by 2?

ii) What number of are divisible by 3?

2. How low are you able to go?

What’s the smallest even quantity between 1000 and 9999 written with 4 totally different digits?

3. All about me

An autobiographical quantity is one the place the primary digit describes what number of 0s it has, the second digit describes what number of 1s it has, and so forth, in order that the (n + 1)th digit describes what number of n’s it has. For instance, 1210 is an autobiographical quantity as a result of it has 1 zero, 2 ones, 1 two and 0 threes.

Discover the one ten digit autobiographical quantity.

I’ll be again at 5pm UK with the options.

PLEASE NO SPOILERS – as an alternative inform me why you discover 108 such an amazing quantity!

Exploring the Great thing about Fascinating Numbers by Shyam Sunder Gupta is out now.

I’ve been setting a puzzle right here on alternate Mondays since 2015. I’m at all times on the look-out for nice puzzles. If you need to counsel one, e mail me.

Sources of as we speak’s puzzles: 1) Leon Gelkoff, 2) SmartFriends, a each day IQ problem, smartfriends.app.hyperlink 3) An outdated basic.