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Suppose that A, B, and C are non-zero distinct digits less than 6, and suppose we have A_6 + B_6 = C_6 and B _6 + B_6 + C_6 = AA_6. Find the three-digit number ABC. (Interpret as a base-6 number with digits A and B, not as A times B. The other expressions should be interpreted in this way as well).

 Jun 10, 2021
 #1
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I just looked through the options and only one worked.

 

A+B<6

so   1<=A<=4           1<=B<=4         2<=C <= 5

 

 Jun 11, 2021

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