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In the following equation, replace x ,y and z with some digits (eg. 1,2,3 etc) and "?" and "!" with some mathematical operator (eg. +-*/), so that the equation hols true

xz ? xy = zx ! xy

This equation has only two known solutions

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  On 7/28/2010 at 12:29 PM, sak_lko said:

In the following equation, replace x ,y and z with some digits (eg. 1,2,3 etc) and "?" and "!" with some mathematical operator (eg. +-*/), so that the equation hols true

xz ? xy = zx ! xy

This equation has only two known solutions

Are x, y and z nonzero? If not, then...

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01 * 05 = 10 - 05

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There is no stipulation that x,y,z must be unique (or that ! and ? are unique).

So the entire set of cases where x=y=z and !=? are all valid solutions.

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15 + 18 = 51 - 18

27 - 24 = 72 / 24

28 + 27 = 82 - 27

49 - 47 = 94 / 47

If you include leading zeros

01 * 05 = 10 - 05

09 + 06 = 90 / 06

02 + 09 = 20 - 09

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If we allow x, y and z and/or the arithmetic operations to not be distinct, and/or allow leading zeroes, we have many solutions.

I believe sak_iko meant that x ≠ y, x ≠ z, y ≠ z; x > 0; z > 0; and ? ≠ !.

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{(1, 8, 5), (+, -)} :: 15 + 18 = 51 - 18 = 33

{(2, 7, 8), (+, -)} :: 28 + 27 = 82 - 27 = 55

{(2, 4, 7), (-, /)} :: 27 - 24 = 72 / 24 = 3

{(4, 7, 9), (-, /)} :: 49 - 47 = 94 / 47 = 2

Edited by Dej Mar
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X,Y and Z are non-zero and not equal. I have thought about two solutions

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27 - 24 = 72 / 24

49 - 47 = 94 / 47

The other two correct solutions are provided by Kevink and Dejmar

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28 + 27 = 82 - 27

15 + 18 = 51 - 18

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