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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
B C Gold 1 2 3 Silver Fair division 11 10 17 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
Gold 1 2 3 Silver Fair division 11 10 17 G G G G G G G G S S G S S S S S S S S S S B picks section I C picks section II A is given section III B C A
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Second Try: A divides island into 3 equal sections
B C Gold 1 2 3 Silver Fair division 11 10 17 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 I II
B C Gold 1 2 3 Silver Fair division 11 10 17 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
Gold 1 2 3 Silver Fair division 11 10 17 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’s section B’s section C’s section A’s value 11 B’s value 12 C’s value 19
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Final division A is envious of C A’s section B’s section C’s section
Gold 1 2 3 Silver Fair division 11 10 17 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’s section B’s section C’s section A’s value 11 9 13 B’s value 7 12 C’s value 19 A is envious of C
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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
Gold 1 2 3 Silver Fair division 11 10 17 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
Gold 1 2 3 Silver Fair division 11 10 17 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
B C Gold 1 2 3 Silver Fair division 11 10 17 A views remainder as worth 28, C views remainder as worth 36 A and C now use divide-and-choose. A divides remainder into two pieces worth 14 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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C values left piece at 22 and right piece at 14
B C Gold 1 2 3 Silver Fair division 11 10 17 C values left piece at 22 and right piece at 14 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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C values left piece at 22 and right piece at 14
B C Gold 1 2 3 Silver Fair division 11 10 17 C values left piece at 22 and right piece at 14 C chooses left piece A gets right piece 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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Final Division A’s section B’s section C’s section A’s value 14
Gold 1 2 3 Silver Fair division 11 10 17 B C A G G G G G G G G S S G S S S S S S S S S S A’s section B’s section C’s section A’s value 14 B’s value 10 C’s value 22
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Final Division B is envious of C A’s section B’s section C’s section
Gold 1 2 3 Silver Fair division 11 10 17 B C A G G G G G G G G S S G S S S S S S S S S S A’s section B’s section C’s section A’s value 14 5 B’s value 7 10 13 C’s value 15 22 B is envious of C
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