Henry Ernest Dudeney/Puzzles and Curious Problems/145 - The Printer's Problem/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $145$

The Printer's Problem

A printer had an order for $10 \, 000$ bill forms per month,

but each month the name of the particular month had to be altered:

that is, he printed $10 \, 000$ "JANUARY", $10 \, 000$ "FEBRUARY", $10 \, 000$ "MARCH", etc.;

but as the particular types with which these words were to be printed had to be specially obtained, and were expensive,

he only purchased just enough movable types to enable him, by interchanging them,

to print in turn the whole of the months of the year.

How many separate types did he purchase?

Of course, the words were printed throughout in capital letters, as shown.

Solution

$\text A, \text A, \text B, \text C, \text D, \text E, \text E, \text E, \text F, \text G, \text H, \text I, \text J, \text L, \text M, \text N, \text O, \text O, \text P, \text R, \text R, \text S, \text T, \text U, \text U, \text V, \text Y$

Proof

You need at least as many of a particular letter as it appears in any given month.

Hence, for example:

$2 \times \text A$ as it appears twice in JANUARY

$3 \times \text A$ as it appears $3$ times in both SEPTEMBER and DECEMBER

$2 \times \text U$ as it appears twice in AUGUST

and so on.

The details are tedious.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $145$. -- The Printer's Problem
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $217$. The Printer's Problem