# Sunday Times Teaser 2899 – Base Jumping

*by Stephen Hogg*

#### Published April 15 2018 (link)

In written multiplication tests Jay always calculated correct answers, but, quirkily, wrote the digits of any two-figure answers in reverse order. A completed test sheet (pre-printed with ordered triplets of single-figure positive integers to multiply, eg, 1x2x2= and 3x5x9=) included a question and his two-figure written answer that would be right when thought of in a number base other than ‘base 10’ (any numerals keeping their usual values). Jay told Kay about this, but didn’t give the question or answer. Kay asked whether one of that question’s numbers to multiply was a particular value and from the reply knew both the question and the answer Jay had written.

What was Jay’s written answer to that question?

My code is similar to Brian’s, but I think we need to consider if Kay received a “No” answer, so I record the potential solutions by each divisor and a Yes/No answer before looking for a unique key.

In the end there is only one possible solution, where Kay asks about the digit 4, and receives a “Yes” answer.

I found it curious that we are asked to submit Jay’s written answer, which can refer to multiple possible written questions, rather than the three digits of the written question, which are unique (and from which we can determine Jay’s answer).