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Island Division: Lone-divider Method
G G G G G G G G S S G S S S S S S S S S S A B C Gold 1 2 3 Silver Total 33 30 51 Fair division 11 10 17
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A divides island into 3 equal sections
G G G G G G G G S S G S S S S S S S S S S I II III A 11 I II III B 10 C 17 B and C happy with any section
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Everyone’s Happy! B picks section I C picks section II
A is given section III G G G G G G G G S S G S S S S S S S S S S B C A
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Second Try: A divides island into 3 equal sections
G G G G G G G G S S G S S S S S S S S S S I II III A 11 I II III B 16 7 C 25 13 B and C only satisfied with Section I
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C divides into 2 equal sections
A is given section III I and II are combined New area worth: 23 to B 38 to C C divides into 2 equal sections G G G G G G G G S S G S S S S S S S S S S A I II I II B 12 11 C 19
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Final division A’s section B’s section C’s section A’s value 11
B’s value 12 C’s value 19 G G G G G G G G S S G S S S S S S S S S S A B C
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Final division A is envious of C! Not envy free A’s section
B’s section C’s section A’s value 11 9 13 B’s value 7 12 C’s value 19 G G G G G G G G S S G S S S S S S S S S S A B C A is envious of C! Not envy free
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Island Division: Last-diminisher Method
G G G G G G G G S S G S S S S S S S S S S A B C Gold 1 2 3 Silver Total 33 30 51 Fair Division 11 10 17
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A cuts section worth 11 to him, and gives it to B
B views it worth 16 which he thinks is too much (should be worth 10) G G G G G G G G S S G S S S S S S S S S S A
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B trims area down to 10 and gives to C
C thinks it’s only worth 15 and lets B keep it G G G G G G G G S S G S S S S S S S S S S B
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A views remainder as worth 28, C views remainder as worth 36
A divides remainder into two pieces worth 14 each and passes the one on the left to C G G G G G G G G S S G S S S S S S S S S S B A
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C thinks piece is worth 22 (too much) and trims it to 18
G G G G G G G G S S G S S S S S S S S S S B A
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C thinks piece is worth 22 (too much) and trims it to 18
C is last diminisher so gets this piece G G G G G G G G S S G S S S S S S S S S S B C
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C thinks piece is worth 22 (too much) and trims it to 18
B C A C thinks piece is worth 22 (too much) and trims it to 18 C is last diminisher so gets this piece, and A gets what’s left G G G G G G G G S S G S S S S S S S S S S
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Final Division A’s section B’s section C’s section A’s value 18
B’s value 10 C’s value B C A G G G G G G G G S S G S S S S S S S S S S
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Final Division B is envious of C! A’s section B’s section C’s section
A’s value 18 5 10 B’s value 9 11 C’s value 15 B C A G G G G G G G G S S G S S S S S S S S S S B is envious of C!
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