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# No. 17

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Replace the same characters by the same numerals so that the mathematical operations are correct.

THC = (T + H + C) x T x H x C

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No. 17 - solution

135 = (1 + 3 + 5) x 1 x 3 x 5

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• 5 months later...

i like this one, but it does take some work (which i decided not to show). like #18, there are two solutions, but only one of the two has distinct digits:

135 = (1 + 3 + 5) * 1 * 3 * 5

and

144 = (1 + 4 + 4) * 1 * 4 * 4

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i like this one, but it does take some work (which i decided not to show). like #18, there are two solutions, but only one of the two has distinct digits:

135 = (1 + 3 + 5) * 1 * 3 * 5

and

144 = (1 + 4 + 4) * 1 * 4 * 4

Leave some for me, will you, guderman?

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• 3 months later...

THC = (T + H + C) x T x H x C

This is the same thing as saying:

THC = (T+H+C)*(THC)

Algebraically, then:

THC/THC = T + H + C

Therefore,

1 = T + H + C

And by substitution then:

1 = (1)*(THC)

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• 2 months later...
THC = (T + H + C) x T x H x C

This is the same thing as saying:

THC = (T+H+C)*(THC)

Algebraically, then:

THC/THC = T + H + C

Therefore,

1 = T + H + C

And by substitution then:

1 = (1)*(THC)

THC != T*H*C

THC is a single number composed of three digits; T, H, and C.

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• 4 months later...

The number THC in algebra, where T H and C are integers is -

100T + 10H + C so the equation is

100T + 10H +C = (T + H + C)THC

but the problem is you need two other equations to find the values of T, H and C

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• 2 years later...

How can this be shown mathematically? Can anyone care to explain please? I am interested in knowing the method of solution.

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