Quandaries and Queries


In the following problem, if the letters A, B, C and D represent some number, what numbers would they represent so that:


Name: Dee

Level: Elementary
Submitted by: Other



Hi Dee,

You have four numbers A, B, C and D and you know that

A times B times C times D times 4 = D times C times B times A What I see first is that if A = 0 then both sides of the equation are zero and hence equal. Thus if A = 0 then whatever values B, C and D have, the equation is true. The same is true if B = 0, or C = 0 or D = 0. Thus if one of the 4 numbers A, B, C or D is zero then the equation is true.

What happens if none of them is zero? In this case if you multiply A, B, C and D together you get some non-zero number. I am going to call this number K. Then the equation is

K 4 = K But if K is not zero then 4  K can't possibly be K and hence the equation is not true.

Thus the only way that ABCD*4 = DCBA can be true is if at least one of A, B, C or D is zero.


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