Using your Head is Permitted

October 2012 riddle

The following riddle was sent to me by Graham Hemsley. It is a delightful variation on a classic riddle. (Familiarity with the original riddle does not count as prior knowledge per se for this month's riddle.)

Thanks Graham! (Other credits will be given on the solution page.)

Graham writes:

    "S is a subset of the real numbers that is closed under addition and subtraction; i.e. if x and y are in S then x+y and x-y are also in S. A value that is in S will be referred to below as 'Compliant'.

    A large rectangle is completely divided into a number of small rectangles. For each of the small rectangles, one or the other of its dimensions is Compliant.

    Prove that one of the dimensions of the large rectangle is Compliant."

Good luck!

List of solvers:

Joseph DeVincentis (31 October 06:51)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


To solution

Back to main page