# Problem of the Month(March 2019)

Given a set {ai} of no more than 5 non-negative integers, are there chess positions with white to move that are identical except for one white piece on a certain square, where there is a mate in ai moves depending on the variable piece? If there are such positions, what is the smallest board they will fit on? Of those, which use the fewest pieces?

Maurizio Morandi and George Sicherman sent solutions.

Here are the best known answers:

White Variable Piece
mate
in
01234
1
(GS)
2
(GS)
(GS)
3
(GS)
(GS)
(GS)
4
(GS)
(GS)
(MM)
(MM)
5
(GS)
(GS)
(GS)
(GS)
(GS)
6
(GS)
(GS)
(GS)
(GS)
(GS)
7
(GS)
(GS)
(GS)
(GS)
(GS)
8
(GS)
(GS)
(GS)
(GS)
(GS)
9
(GS)
(GS)
(GS)
(GS)
(GS)
10
(GS)
(GS)
(GS)
(GS)
(GS)

{0,1,2} (GS)
{0,1,3} (GS)
{1,2,3} (GS)
{1,2,4} (GS)
{1,3,4} (GS)
{2,3,4} (GS)
{1,3,5} (GS)
{3,6,9} (GS)
{0,1,2,3} (GS)
{1,2,3,4} (GS)
{1,2,4,8} (GS)

Black Variable Piece
mate
in
1234
2
(GS)
3
(MM)
(MM)
4
(GS)
(GS)
(MM)
5
(GS)
(GS)
(GS)
(GS)
6
(GS)
(GS)
(GS)
(GS)
7
(GS)
(GS)
(GS)
(GS)
8
(GS)
(GS)
(GS)
(GS)
9
(GS)
(GS)
(GS)
(GS)
10
(GS)
(GS)
(GS)
(GS)

{1,2,3} (MM)
{1,2,4} (GS)
{1,3,4} (GS)

{2,3,4} (GS)
{2,4,6} (GS)
{1,2,3,4} (GS)

If you can extend any of these results, please e-mail me. Click here to go back to Math Magic. Last updated 3/17/19.