An optimisation problem with letters

Browsing in a local craft shop the other day, I spotted this sheet of rub-down letters.  I happened to have a camera with me.

Letters for card making and other craftwork

Several aspects of this sheet are interesting.  First, the designer has not taken any account of the frequency of appearance of different letters in the English language.  There are two of each letter, numeral and symbol, except there are three "I"s and one "?".  Purchasers are going to have a lot of waste, unless they create cards with pangrams such as "Cwm fjord bank glyphs vext quiz".  You can't write "Happy birthday David" with the selection here.

Second, there has been a slight attempt to optimise the packing of letters; look at the inverted "A" and "7" which mean that the two examples of these are closer together than if both were upright.  But, if this was a genuine attempt to pack the letters, why not use the same idea to pack the "J", "L" and "W".  Possibly also the "Y", "V" and "T"? 

Third, why is it necessary to keep the letters in strict alphabetical order?  One could imagine a layout with the letters packed more tightly if the designer could deviate slightly from strict order, as has been done with the letter"I"

Fourth, what is the constraint here?  Is it the size of sheet?  Was the designer told to pack the letters onto a given size sheet, and make the letters as large as possible while supplying two complete alphabets?  Or was the designer given the size of the letters, and told to pack them onto as small a sheet as possible?  I suspect that the sheets are of a standard size, so that the letters have been made as large as possible.

Starting from 1959, before personal computers, a company called Letraset made rub-down letters and symbols which were used by designers, magazine editors, artists, engineers and architects.  Their sheets had different numbers of the letters.

A sample of Letraset 

Again, these sheets were of standard sizes, so the number of letters and symbols was optimised for each point size; it would be interesting to know how the numbers were chosen.  I remember that as teenage schoolboys, we enjoyed collecting the give-away samples of Letraset from a local stationery shop.

O.R. has contributed several algorithms for packing objects; I wonder whether they have reached designers of craft materials?


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