# Solution

(related to Problem: Fifteen Letter Puzzle)

The following will be found to comply with the conditions of grouping:—

$$\begin{array}{cccc} A L E & M E T & M O P & B L M\\ B A G&C A P&Y O U&C L T\\ I R E&O I L&L U G&L N R\\ N A Y&B I T&B U N&B P R\\ A I M&B E Y&R U M&G M Y\\ O A R&G I N&P L Y&C G R\\ P E G&I C Y&T R Y&C M N\\ C U E&C O B&T A U&P N T\\ O N E&G O T&P I U\\ \end{array}$$

The fifteen letters used are $A, E, I, O, U, Y,$ and $B, C, G, L, M,$ $N, P, R, T.$ The number of words is $27,$ and these are all shown in the first three columns. The last word, $PIU,$ is a musical term in common use; but although it has crept into some of our dictionaries, it is Italian, meaning "a little; slightly." The remaining twenty-six are good words. Of course, a $TAU$-cross is a $T$-shaped cross, also called the cross of St. Anthony, and borne on a badge in the Bishop's Palace at Exeter. It is also a name for the toad-fish.

We thus have twenty-six good words and one doubtful, obtained under the required conditions, and I do not think it will be easy to improve on this answer. Of course, we are not bound by dictionaries but by common usage. If we went by the dictionary only in a case of this kind, we should find ourselves involved in prefixes, contractions, and such absurdities as I.O.U., which Nuttall actually gives as a word.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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