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Missing Duodecimal Digit Determination (Posted on 2022-08-04)

If the duodecimal number A7?B5? is divisible by (83)_{base 12}, then determine the missing digits.
** Each question mark represents a duodecimal digit, whether same or different.

See The Solution Submitted by K Sengupta

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solution

| Comment 1 of 6

Let missing digits equal X and Y so base-12 A7?B5? becomes base-10

10*12^5 + 7*12^4 + X*12^3 + 11*12^2 + 5*12 + Y.

The divisor is base-12 83 which is 99=9*11 base-10.

To be divisible by 9 requires 60 + Y divisible by 9 so Y=3.

B and A are respectively 11 and 10 in base ten. Therefore, to be divisible by 11 requires 10+7+X+63 divisible by 11 so x=8.

The duodecimal number is then A78B53 which equals decimal 2648943=99*26757

***edited per request by puzzle author***

Edited on August 5, 2022, 12:50 pm

Posted by xdog on 2022-08-04 09:08:51

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