# Solution

(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.

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### References

#### Project Gutenberg

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

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