1. Hundred means 120.

The word “hundred” comes from Old Norse hundrath, which actually meant 120 due to the duodecimal system

2.

Guess Your Age.

Ask someone to multiply the first digit of their age by 5, add 3, double it, add the second digit of the age, and subtract 6. Reveal their age using math tricks.

3. Kaprekar’s Constant (6174).

• 6174 is known as Kaprekar’s Constant, named after Indian mathematician D. R. Kaprekar.
• It’s a fixed point reached by repeatedly rearranging the digits of a four-digit number into ascending and descending order, then subtracting the smaller from the larger.
• No matter which four-digit number you start with (as long as not all digits are the same), the process converges to 6174 in at most 7 steps.

The Kaprekar Routine

1. Choose a four-digit number (e.g., 3524).
2. Rearrange digits into largest (5432) and smallest (2345).
3. Subtract: 5432 – 2345 = 3087.
4. Repeat with 3087 → 8730 – 0378 = 8352.
5. Continue until you reach 6174.
6. Once at 6174, the process stays there: 7641 – 1467 = 6174.

4. Amicable Numbers.

Amicable numbers are pairs of numbers where each number is the sum of the other’s proper divisors (excluding the number itself).

The lowest pair of amicable numbers are:-   220 and 284.

Proper divisors of 220 – 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 – added together = 284

Proper divisors of 284 – 1, 2, 4, 71, 142 – added together = 220

The mathematical formula:-

Two different numbers a and b form an amicable pair if:

s(a)=b and s(b)=a

Amicable numbers are rare.

The next four lowest pairs are:-

• (1,184, 1,210)

  • Sum of proper divisors of 1,184 = 1,210

  • Sum of proper divisors of 1,210 = 1,184

• (2,620, 2,924)

  • Sum of proper divisors of 2,620 = 2,924

  • Sum of proper divisors of 2,924 = 2,620

• (5,020, 5,564)

  • Sum of proper divisors of 5,020 = 5,564

  • Sum of proper divisors of 5,564 = 5,020

• (6,232, 6,368)

  • Sum of proper divisors of 6,232 = 6,368

  • Sum of proper divisors of 6,368 = 6,232

5. How many neurons?

86 billion: Approximate neurons in the human brain.