Can you solve it? The world’s most fascinating number – revealed! | Mathematics

Before arriving at today’s puzzles, I would like to present the most interesting number in the universe.

108

Readers of Asian heritage will nod with familiarity. The number is of deep importance in Hinduism, Jainism, Sikhism, Buddhism and Chinese culture. This is the number of pearls on a rosary, the number of sun greetings carried out during a yoga ceremony, the number of Buddhas to be drunk for good luck and the telephone number of the Indian Emergency ambulance service.

Mathematically, 108 is also a superstar, a fact that I only recently discovered in a new book by the former principal engineer of Indian railways, Slayam Sound Gupta. For example:

108 is 1¹ x 2² x 3³ The product of the first three figures raised for themselves.

108 is the smallest number whose dividers when taken together contain each figure at least once. (The dividers are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108)

108 is the biggest known number n such that 2ⁿ does not contain 9.

(2¹⁰⁸ = 324518553658426726783156020576256)

108 is the internal angle (in degrees) of an ordinary pentagon

108 is the number of free heptomins (Tetris type forms made from seven linked squares.)

108 is the number of cards in a UNO deck.

I only scraped the surface. Gupta’s book, Explore the beauty of fascinating numbers, At ten pages of facts around 108, ending with the observation that “1” represents the truth, “0” for the void and “8” is the symbol of the infinite turned of 90 degrees. “Thus, the sacred number 108 tells us that we are both something, nothing and everything.” The only other numbers to which Gupta devotes an entire chapter are PI, 13, 666 and 153 (perhaps the second most interesting number in the universe).

The spiritual importance of 108 could have led Asian mathematicians to catalog interesting properties on this subject. Or it may be that 108 is really a particularly interesting number – it is not too small, not too large and very divisible – which helped him gain spiritual importance in the first place. How good that numerologists and theorists of numbers have something to be suitable for once!

Today’s puzzles concern figures with interesting properties.

1.

You have ten cards. On each of the cards, there is one of the figures 0 to 9. When you organize the cards in a line, you get a number between 0123456789 and 9876543210.

i) How many of these figures are divisible by 2?

ii) How many are divisible by 3?

2. How much can you go?

What is the smallest peer number between 1000 and 9999 written with four different figures?

3. All about me

An autobiographical number is that where the first figure describes how many 0s it has, the second figure describes the number of 1, and so on, so that the (N + 1) The number describes how much n ‘If he has. For example, 1210 is an autobiographical number because it has 1 zero, 2, 1 two and 0 three.

Find the only ten -digit autobiographical number.

I will be back at 5 p.m. from the United Kingdom with the solutions.

Update: Read the solutions here.

Please don’t spoil – tell me more why you find a large number of a number!

Exploring the beauty of the fascinating numbers of SHYAM SENDER GUPTA has now been released.

I have been putting a puzzle here on alternative Mondays since 2015. I am still looking for big puzzles. If you want to suggest one, send me an email.

Sources of today’s puzzles: 1) Leon Gelkoff, 2) Smartfriends, a daily challenge of Qi, smartfriends.app.Link 3) An old classic.