MathDB

On a line,

44

points are marked and numbered

1, 2, 3,…,44

from left to right. Various crickets jump around the line. Each starts at point

1

, jumping on the marked points and ending up at point

44

. In addition, each cricket jumps from a marked point to another marked point with a greater number. When all the crickets have finished jumping, it turns out that for pair

i, j

with

{1}\leq{i}<{j}\leq{44}

, there was a cricket that jumped directly from point

i

to point

j

, without visiting any of the points in between the two. Determine the smallest number of crickets such that this is possible.

Problem Statement