A Puzzle on Leap Frog Jumping Board

A Puzzle on Leap Frog Jumping
(With a surprising result) By N.D.Prabhakar

Board: Men placed at grid points

• A jump move involves two adjacent pieces (men) along same row or same column • No cross-wise jump • After a jump, the man must land on a vacant position, and the man who is jumped over gets removed from the board • A piece can jump over only one piece in one move

Red , Yellow and Violet pieces can not jump Green can jump right over blue Blue can jump left over green Blue can jump up over yellow Blue can jump down over violet

Levels
ETC. above Level 3

Level 2
Level 1 Level 0 Level -1 ETC. below

Problems
• Designate one of the rows as Level 0, and rows above that as Levels 1,2,3, etc. • You are allowed to place as many men as you need in any configuration of your choice in Level 0 and below (board potentially infinite) • How many men would you need in order to reach a man to level k using leap frog jumping moves, for k=1,2,3,… ?

Reaching Level 1
• Needs two men

Level 0

Reaching Level 1
• Blue piece jumps over green piece: green shown crossed out

Level 1 Level 0

Reaching Level 2
• Needs 4 men

Level 2 Level 1

Level 0

Reaching Level 2
• 1st move: Blue jumps up over green

Level 2 Level 1

Level 0

Reaching Level 2
• 2nd move: Red jumps right over green

Level 2 Level 1

Level 0

Reaching Level 2
• 3rd move: Red jumps up over blue

Level 2 Level 1

Level 0

Reaching Level 3
• Needs 8 men
Level 3 Level 2 Level 1 Level 0

Reaching Level 3
• In 3 moves we saw before, get the blue piece to level 2
Level 3 Level 2 Level 1 Level 0

Reaching Level 3
• In moves 4 and 5, get the violet and yellow pieces jump left
Level 3 Level 2 Level 1 Level 0

Reaching Level 3
• In move 6, yellow pieces jumps up over violet

Level 3 Level 2 Level 1 Level 0

Reaching Level 3
• In move 7, yellow piece jumps up over blue

Level 3 Level 2 Level 1 Level 0

Reaching Level 4
• Need 20