Problem: A Puzzle in Reversals

Most people know that if you take any sum of money in pounds, shillings, and pence, in which the number of pounds (less than £$12$) exceeds that of the pence, reverse it (calling the pounds pence and the pence pounds), find the difference, then reverse and add this difference, the result is always £$12$, $18$s. $11$d. But if we omit the condition, "less than £$12,$" and allow naught to represent shillings or pence—

  1. What is the lowest amount to which the rule will not apply?
  2. What is the highest amount to which it will apply?

Of course, when reversing such a sum as £$14,$ $15$s. $3$d. it may be written £$3,$ $16$s. $2$d., which is the same as £$3,$ $15$s. $14$d.

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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