MathDB

Fix an integer

n \ge 2

and let

A

be an

n\times n

array with

n

cells cut out so that exactly one cell is removed out of every row and every column. A stick is a

1\times k

k\times 1

subarray of

A

, where

k

is a suitable positive integer. (a) Determine the minimal number of sticks

A

can be dissected into. (b) Show that the number of ways to dissect

A

into a minimal number of sticks does not exceed

100^n

.
proposed by Palmer Mebane and Nikolai Beluhov
[hide=a few comments]a variation of part a, was [url=https://artofproblemsolving.com/community/c6h1389637p7743073]problem 5 a variation of part b, was posted [url=https://artofproblemsolving.com/community/c6h1389663p7743264]here this post was made in order to complete the post collection of RMM Shortlist 2017

Problem Statement