perplexus.info :: Just Math : Identical Digit Baffle

Identical Digit Baffle (Posted on 2014-09-08)

Determine the largest five digit base-14 positive integer such that when multiplied by a single base-14 digit, the result is a six digit base-14 positive integer with all digits identical.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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calculator solution

Comment 2 of 2 |

111111 (base 14) = 579195 (base 10) = 3^2*5*61*211,

so the single base 14 digit associated with the largest 5 digit solution is either 3 or 5 or 9.

8/9 is bigger than 2/3 or 4/5, so the final answer is

(8/9)*579195 = 514840 (base 10) = D58A4 (base 14)

Posted by Steve Herman on 2014-09-08 21:48:53

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