Join the Guessing Game
Logic
Level
2
Sam asked Tim to play a guessing game where the former will be the one who'll be guessing. This is how they played it:
- Tim thought of two consecutive positive integers and didn't tell them to Sam.
- Sam thought of a positive integer and tells it to Tim.
- Tim added his smaller number to Sam's number and didn't tell the sum.
- Tim subtracted the sum to his larger number and didn't tell the difference.
Sam was able to figure out the difference without knowing Tim's original two numbers.
What is the difference?
more than Sam's number
more than Tim's larger number
less than Tim's smaller number
less than Sam's number
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1 solution
Let's say that Sam's number is S while Tim's numbers are T and T + 1 . At first, Tim added his smaller number to Sam's number.
S + T
Next, Tim subtracted the sum to his larger number.
( S + T ) − ( T + 1 ) = ( S + T ) + ( − T − 1 ) = S − 1
The T above cancels out since adding two numbers with opposite signs will give 0 . So this leaves us with 1 less than Sam’s number .