Each player can remove 1 or 2 pegs. Player who removes the last peg wins

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Presentation transcript:

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

420 411 321 410 401 320 311 221 400 310 301 220 211 121 4 2 1 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

Determining P and N positions

421 Winning move! 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

421 Winning move! 420 411 321 410 401 320 311 221 4 2 1 400 310 301 220 211 121 Each player can remove 1 or 2 pegs. Player who removes the last peg wins. 300 210 201 120 111 021 200 110 101 020 011 100 010 001 000

17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 P- and N- positions in substraction game with subtraction set {2, 5, 8}. From state K there is a transition to the states K2, K5 and K8 (if those are non-negative).

Generate P and N positions in the subtraction game with substraction set {2, 5, 8}. 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 8 5 2 8 2 5 8 2 5 8 2 5 8 2 5

Generate P and N positions in the subtraction game with subtraction set {2, 5, 8}. 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 8 2 5 8 2 5 8 2 5 8 2 5 8 2 5 8 2 5 etc...