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A repunit product (Posted on 2017-08-19) Difficulty: 3 of 5
TOP*SPA=(a 6-digit number)

There are numerous valid words yielding valid solutions,
but only one product consists of a chain of the same digit repeated 6 times!

This is the one we want!

Use of software not recommended, it is easily solvable by logical deduction.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 4
The prime factors of 111111 are 3, 7, 11, 13 and 37. These must be present in TOP combined with SPA, possibly with another prime or semiprime that is the repeated digit.

First let's assume that 11 is combined in either TOP or SPA with 13 or 37:

11*13=143; if another factor then: 286, 429,  572, 715, 858 
11*37=407; if another factor then: 814

Neither TOP nor SPA can be 858. If using another factor that factor would have to be 2, 3, 4 or 5. If 3, that could be either the repdigit or the 3 in the factorization of 111111.

In the first case (143 and multiples) what's left are 3*7*37=777, also not TOP or SPA. But if the 3 has been used by the 143*3=429, 7*37=259, or one if its multiples: 518 or 777.

Let's try 407 or 814: It leaves 3*7*13=273.

407 * 273 = 111111, which fits the alphametic.

  Posted by Charlie on 2017-08-19 22:04:28
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