# Sunday Times Teaser 2686 – Good Innings

*by H. Bradley and C. Higgins*

Pat started a tour of public houses, all of which had the same admission charge of a four digit number of pence. When the order of its digits is reversed this charge was equal to the number of pence that Pat had at the start of his tour.

In the first public house, Pat spent one one Pound less than a third of what he had left after paying to enter. In the second public house, he again spent one Pound less than a third of what he had left after paying the admission charge. This left him only enough to pay to enter the third public house.

How much was the admission charge?

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Sadly another very simple teaser that is not a programming challenge.

If x is the admission charge and y is Pat’s starting money, then the spending in the first inn is (y – x) / 3 – 100. Spending in the second in is then (y – 2x – ((y – x) / 3 – 100)) / 3 – 100. This gives:

x = y – 2x – ((y – x) / 3 – 100) – ((y – 2x – ((y – x) / 3 – 100)) / 3 – 100)

and hence 19x = 4y + 1500 as a result of which we can get the answer by trial and error.