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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).

 Apr 8, 2022
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Let  A = 1,  B = 2, and  C = 3.

 

A6 + B6  =  C6     --->     16 + 26  =  36

 

B6 + B6 + C6  =  AA6     --->     26 + 26 + 36  =  116  

 

ABC6  =  1236     which, in base ten, is:  1·62 + 2·6 + 3  =  51

 Apr 8, 2022

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