# Solution

(related to Problem: Hannah's Puzzle)

Starting from any one of the $N$'s, there are $17$ different readings of $NAH,$ or $68$ ($4\times 17$) for the $4$ $N$'s. Therefore there are also $68$ ways of spelling $HAN.$ If we were allowed to use the same $N$ twice in a spelling, the answer would be $68\times 68,$ or $4,624$ ways. But the conditions were, "always passing from one letter to another." Therefore, for every one of the $17$ ways of spelling $HAN$ with a particular $N,$ there would be $51$ ways ($3\times 17$) of completing the $NAH,$ or $867$ ($17\times 51$) ways for the complete word. Hence, as there are four $N$'s to use in $HAN,$ the correct solution of the puzzle is $3,468$ ($4\times 867$) different ways.

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@H-Dudeney

### References

#### Project Gutenberg

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

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.