If `f:{1,2,3,4} ->{1,2,3,4}`, y = f(x) be a function such that `|f(alpha) - alpha| <1` for `alpha in {1,2,3,4}` then total number of functions are

Explanation

Here, `f(alpha) = |f(alpha) - alpha| le 1` for `alpha in {1,2,3,4}`

`:. f(1) = |f(1) - 1| le 1 = {1,2}`

`:. f(2) = |f(2) - 2| le 1 = {1,2,3}`

`:. f(3) = |f(3) - 3| le 1 = {2,3,4}`

`:. f(4) = |f(4) - 4| le 1 = {3,4}`

Here, `f(1)` and `f(4)` contains `2` functions each and `f(2)` and `f(3)` contains `3` functions each.

`:.` Total number of functions ` = 2**3**3**2 = 36`.