1. Our school’s puzzle-club meets in one of the schoolrooms every Friday after s
ID: 1721315 • Letter: 1
Question
1. Our school’s puzzle-club meets in one of the schoolrooms every Friday after school. Last Friday, one of the members said, “I’ve hidden a list of numbers in this envelope that add up to the number of this room.” A girl said, “That’s obviously not enough information to determine the number of the room. If you told us the number of numbers in the envelope and their product, would that be enough to work them all out?”
He (after scribbling for some time): “No.” She (after scribbling for some more time): “well, at least I’ve worked out their product.” What is the number of the school room we meet in?”
Explanation / Answer
It is not possible to determine the room number using just the number of numbers and their product.
Here is a counter example :
Say there are three numbers inside the envelope x, y and z .And say their product be 24. Then we can set an equation xyz=24 . Now this is possible for x=1 ,y=2 and z=12 (in this case room number will be 1+2+12=15) and it is also possible for x=2 ,y=3 and z=4 (in this case the room number will be 2+3+4=9).
Likewise there can be other possibilities as well. Hence, we cannot determine the room number.
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