What is the minimum number of condoms required for safe sex in each case: (a) two men with two women (b)...
logic/condoms
Problem
What is the minimum number of condoms required for safe sex in each case: (a) two men with two women (b) one man with three women or three men with one woman (c) three men with each other (d) 2k+1 men with one woman (e) m men and n women
Show solution
A, B, C, etc. refers to people.
1|2 refers to the two sides of the first condom.
3|4 refers to the two sides of the second condom.
etc.
(a) two condoms
A, B = men; C, D = women.
1|2 3|4 A has sex with C. 1 4
1|2 A has sex with D. 1 4 2
3|4 1|2 B has sex with C. 1 3 4 2
3|4 B has sex with D. 1 3 4 2
(b) two condoms
A = man; B, C, D = women. A B C D
1|2 3|4 A has sex with B. 1 4
1|2 A has sex with C. 1 4 2
1|2 4|3 A has sex with D. 1 4 2 3
A, B, C = men; D = woman.
1|2 3|4 A has sex with D. 1 4
3|4 B has sex with D. 1 3 4
2|1 3|4 C has sex with D. 1 3 2 4
(c) two condoms
A, B, C = men.
1|2 3|4 A has sex with B. 1 4
4|3 2|1 B has sex with A. 1 4
3|4 C has sex with B. 1 4 3
4|3 B has sex with C. 1 4 3
1|2 4|3 A has sex with C. 1 4 3
3|4 2|1 C has sex with A. 1 4 3
(d) k+1 condoms
A = woman; B, C, D, ... = men
1|2 A has sex with B. 1 2
1|2 4|3 A has sex with C. 1 2 3
1|2 3|4 A has sex with D. 1 2 3 4
and so on, after the first man there is one condom used for every two men
(e) ceiling(m/2 + 2n/3)
see Ilan Vardi, Computational Recreations in Mathematica, Addison Wesley,
1991, p. 205