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


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@H-Dudeney


References

Project Gutenberg

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

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.