What is the number on the whiteboard?
A math teacher writes a number on the whiteboard. The number is between 1 to 100, both inclusive.
He then assigns all his 10 math students a number from 1 to 10, both inclusive. Each math student receives a unique number.
The math teacher says to the students,
"If the number on the whiteboard is divisible by your assigned number, raise your hand."
7 people raised their hands. If the person with the number 10 did not raise his hand, find the number on the whiteboard.
The answer is 72.
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1 solution
We know the number is not divisible by 10. So the number is not divisible by both 2 and 5.
If the number is not divisible by 2, then the number will not be divisible by 2, 4, 8 and 10. In this case at most 6 people will raise their hands.
So now we know the number is divisible by 2. This means the number is not divisible by 5. So the person with the number 5 will not raise his hand.
Out of the numbers 1, 2, 3, 4, 6, 7, 8, 9, the number is divisible by 7 of these numbers.
If the number is not divisible by 4, there will not be 4 and 8. If the number is not divisible by 3, there will not be 3 and 9. So the number is divisible by 3 and 4, which is 12.
We can now remove the factors of 12 from the list. We are left with 7, 8 and 9.
If the number is divisible by 7, then the number must be 7 x 12, which is 84. However 84 is not divisible by 8 and 9.
So the number must be divisible by 8 and 9, and the only number between 1 to 100 that meets this criteria is the number 72.
So the number on the whiteboard is 72.