Enigma 270: Cubic stamp-sheet
3 April 2015
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From New Scientist #1417, 16th August 1984 [link]
Picnicaria’s independence is to be celebrated by a triumph of technological virtuosity, a Cubic stamp-sheet, which you are asked to design. Let me explain. The “sheet” will look like a cubic die, with a square postage-stamp forming each of the six faces, and with perforations along each of the 12 edges. The whole object of the exercise is to enable the customer to stamp a letter or parcel with a postage of any whole number pence from 1 up to N by tearing along suitable perforations and thus getting a connected set of one or more stamps which add up to exactly the right amount. N is to be made as large as possible.
How large can N be? And what values have the stamps on the various faces?
(The easiest way to specify a layout is to give the values of opposite faces: e.g. a layout like that of an ordinary die is “1/6, 2/5, 3/4”, giving N=21).