Ahmed and Bader play the following game:
Ahmed secretly chooses integers x,y,z valued between 0 and 99 (inclusive), while Bader chooses numbers a,b,c. Bader, then, gives Ahmed his numbers, and Ahmed returns the sum ax+by+cz. Bader wins if he can guess Ahmed’s initial numbers. Is there a selection of a,b,c such that Bader guarantees to win?
Yes, bader Chooses 1, 1, 1, which means ax, by, cz = x, y, z, so ahmed will return his original numbers, which means bader is guaranteed to win 
and the same could be done for any n, bader chooses n, n, n and then divides the returned numbers each by n
I think you miss inderstood the problem, if you choose 1,1,1 you will get x+y+z not x,y,z.
However, you need to choose numbers that simply show you each one of them alone even after summation, so choose 1,100,10000. So you get x+100y+1000z each will be seperate digits
Example if the secret numbers are 7,56, and 60 the sum will be
7+100X56+60X10000= 605607
3 Likes