Henry Ernest Dudeney/Puzzles and Curious Problems/57 - The Broken Clock Face/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $57$

The Broken Clock Face

How may a clock dial with Roman numerals be broken into four parts

so that the numerals on each part add up in every case to $20$?

Solution

There are $13$ solutions in total, exemplified by the one given by Dudeney himself:

Historical Note

Martin Gardner points out, in his $1968$ repackaging 536 Puzzles & Curious Problems, that there are a total of $13$ possible solutions here.

They are all listed in his columns in Scientific American for May and June $1966$, reprinted in his $1975$ collection Mathematical Carnival.

He also notes that the solution given in the first edition of Puzzles and Curious Problems was inferior, requiring that the $\text {IX}$ be viewed upside down and interpreted as $\text {XI}$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $57$. -- The Broken Clock Face
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $49$. The Broken Clock Face