Question

A number between 1 and 100 is written down on a piece of paper. Can you figure out the number based on these clues?
1) Its a two-digit number.
2) The second digit is greater than the first.
3) Its not a Prime number.
4) Its not a perfect square.
5) Its not divisible by 3.
6) It doesn't contain any 8's.
7) The sum of the digits is not a prime number.
8) The sum of the digits is not 8.

Answer 1

46

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Considering first 2 clues we get 2- digit numbers (from 12 to 89) with sum of digits:
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Considering clues 5, 7, 8 we exclude- 3, 5, 7, 8, 11, 13, 17 as prime numbers and sum of digits = 8, we exclude 6, 9, 12, 15 due to divisibility by 3 (sum of digits divisible by 3 means numbers are divisible by 3 too), now left with 4, 10, 14, 16.
Lets see what numbers we have with sum of digits being 4, 10, 14, 16
4--> 13- excluded as prime number
10--> 19, 28, 37, 46- first 3 excluded as prime number and containing 8, left with 46
14--> 59, 68- both excluded as prime number and containing 8
16--> 79- excluded as prime number
So the only number left is 46