[Guest]

Substitute each of the capital letters by a different digit from 0 to 9 to satisfy the following system of cryptarithmetic equations. Each of A, S and B is nonzero.

Y^B – B^Y = AIOO and, O^T – T^O = SIEE and, U^T – T^U = BIOD

[Guest]

Since the LHS is each case is single digit numbers, the only sets of (a,b) for which f(a,b) = a^b - b^a results in 4 digit numbers are: (3,7), (3,8), (4,6) and (5,6)

Of these f(3,7) results in 1844, f(3,8) results in 6049, f(4,6) results in 2800 and f(5,6) results in 7849

As per the given conditions of digit placements then,

Y = 3

B = 7

O = 4

T = 6

U = 5

A = 1

S = 2

D = 9

I = 8

Edited August 27, 2009 by DeeGee

[Gmaster479]

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Edited August 28, 2009 by Gmaster479

[Guest]

Amarnath_Caterpillar

There are 4 combinations of the form X^Y-Y^X that gives 4 digit number.

1.3^8-8^3=6049

2.3^7-7^3=1844

3.4^6-6^4=2800

4.5^6-6^5=7849

Question: Y^B – B^Y = AIOO and, O^T – T^O = SIEE and, U^T – T^U = BIOD

so

Y^B – B^Y = AIOO 3^7-7^3=1844

O^T – T^O = SIEE 4^6-6^4=2800

U^T – T^U = BIOD 5^6-6^5=7849