6 replies to this topic

[rookie1ja]

No. 17 - Back to the Cryptograms and Algebra Puzzles
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

This old topic is locked since solution is already provided in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

No. 17 - solution
135 = (1 + 3 + 5) x 1 x 3 x 5

[guderman]

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

[BoilingOil]

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?

[jimc52]

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)

[Magic]

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.

[AliceJH]

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

[quasi]

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