**From New Scientist #965, 4th September 1975 **[link]

Here is a simple prescription for vertigo. Draw a 4×4 grid (16 cells in a 4×4 array). Write a V in the bottom left corner, an E in each of the two adjacent cells, and R in each of the three empty cells adjacent to an E, a T in each of the four empty cells adjacent to an R, an I in each of the three empty calls adjacent to a T, a G in each of the two empty cells adjacent to an I and an O in the top right corner.

To induce mild vertigo, work out how many ways there are of spelling VERTIGO, starting the the bottom left corner and ending at the top right, as if you were an ant taking exercise. The answer is 20. Feeling better?

Tougher exercise can induce schizophrenia. So start again with a 7×7 grid and repeat the prescription with SCHIZOPHRENIA.

How many ant-like ways are there of spelling that?

[tantalizer415]

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We’ve encountered puzzles similar to this before. See:

Enigma 1465,Enigma 1373,Enigma 1108,Tantalizer 457(and also:Enigma 1711,Teaser 2935,Enigma 1024).Of course this puzzle was published before any of these, but

Tantalizer 457is basically the same puzzle.As you progress through the grid you make 12 steps. 6 of the steps are to the right and 6 are upwards. If you choose the rightward steps, then the remaining steps are the upward ones.

So the number of routes is:

C(12, 6) = 924.Solution:There are 924 different paths.See the code at

Tantalizer 457for a constructive programmatic solution.