(related to Problem: The Level Puzzle)

Let us confine our attention to the $L$ in the top left-hand corner. Suppose we go by way of the $E$ on the right: we must then go straight on to the $V,$ from which letter the word may be completed in four ways, for there are four $E$'s available through which we may reach an $L.$ There are therefore four ways of reading through the right-hand $E.$ It is also clear that there must be the same number of ways through the $E$ that is immediately below our starting point. That makes eight. If, however, we take the third route through the $E$ on the diagonal, we then have the option of any one of the three $V$'s, by means of each of which we may complete the word in four ways. We can, therefore, spell $LEVEL$ in twelve ways through the diagonal $E.$ Twelve added to eight gives twenty readings, all emanating from the $L$ in the top left-hand corner; and as the four corners are equal, the answer must be four times twenty, or eighty different ways.

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



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 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.