1 64 ways of spelling PYRAMID. [With each move down in the triangle you have a binary choice: to deviate to the left or to the right; so the number of routes is 2 (L – 1), where L is the number of levels (or letters). Here L = 7; 26 = 64.]
2 n must be odd (that is, the word must contain an odd number of letters). We need to get from the top to the bottom by shifting leftwards, L, 3 times and rightwards, R, 3 times. The number of ways of doing this is (6!)/(3!) (3!) = 20. [We need the number of distinct arrangements of 3 Ls and 3Rs]. In general we have (n – 1)!/ [((n – 1)/2)!] 2.
Wordpool a) Same Difference SPIN, SPINE