Enigma 312: Six-stamp sheet
25 September 2015
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From New Scientist #1460, 13th June 1985 [link]
They are now printing stamp-books with stamps of different values on the same sheet. Let us take this a stage further, and design a sheet of 3 × 2 stamps, so that you can make up a postage of any whole number of pence from 1 up to N by tearing out a connected set of one or more stamps.
“Connected” means edge-connected, not just corner-touching, so that, for instance, the sheet illustrated achieves only N=5, since neither 4+2 nor 5+1 is a connected set, and so 6 is impossible.
Make a sketch showing how to make N as big as possible, and state what N is.