# Math Challenge

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A three-digit number increases by 9 if we exchange the second and third digits. The same three-digit number increases by 90 if we exchange the first and second digits. By how much will the value increase if we exchange the first and third digits?

• Math Challenge -

well, the second digit must be 9 more than the third. as in 09...or, it is the complement to 9 (as in 1), as in X23,so the switched is X32 (nine more).

Complements: N,N+1 (as in 12, 23, 32, 43, and so on.

Not the second hint..the first and second:
BAx-ABx=90 so a,b must be complements also, as above.

Lets check; 123
first hint: 132-123=9
second hint:213-123=90 checks

Lets check another: 456
first hint: 465-456=9
second hint:546-456=90 checks.
so there are a multitude of answers for what the number is.

In the first case, 321-123=198
in the second case,654-456=198

hmmmm, very interesting. Why don't you try a few more?

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