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# No. 17

6 replies to this topic

### #1 rookie1ja

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Posted 31 March 2007 - 05:10 PM

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

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### #2 guderman

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Posted 26 September 2007 - 10:55 PM

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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### #3 BoilingOil

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Posted 26 September 2007 - 10:57 PM

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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### #4 jimc52

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Posted 13 January 2008 - 08:54 PM

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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### #5 Magic

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Posted 29 March 2008 - 02:16 PM

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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### #6 AliceJH

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Posted 01 August 2008 - 11:43 AM

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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### #7 quasi

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Posted 28 November 2010 - 07:02 PM

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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