Answer to Question #4501 in Quantitative Methods for Aditi
& 9(1000x+y) = 4(1000y+x)
which simplifies to
8996x = 3991y
which on division by 13 becomes
& 692x = 307y
where the coefficients are relatively prime.
This has the obvious solution
& x = 307n, y = 692n for any integer n
The only solution in which x and y are both 3-digit numbers is for
n = 1. Then
& HAT = 307
& BOX = 692
& 9(HATBOX) = 9(307692) = 2769228
& 4(BOXHAT) = 4(692307) = 2769228
The only thing wrong is that A = 0, which violates the conditions.
Since this is the only solution to the equation, there is no solution
to the problem as stated.
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