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This Python program examines all possible combinations of votes. It runs in 1.3s.

Solution:Prunes received 6 votes. Slap received 5 votes. Love received 4 votes. Marriage received 2 votes. Tickell received 1 vote. Custard received no votes.There are 4 possible voting patterns: L voted for L+S+P; M voted for M+P; S voted for L+S+P; T voted for L+P; P voted for M+P; C voted for L+P. Then from the remaining votes cast by M, T, P and C, one of them voted for T and the rest of them voted for S.

Here’s the problem expressed as a set of constraints in a MiniZinc model. It runs finds the four solutions in 77ms (

mzn-gecode -a enigma273.mzn).From the puzzle constraints, it is easy to deduce that

totals for the candidates have to be 0,1,2,4,5,6

6>L>M>1

5>T>C

S>0,

L+M = S+T = P+C = 6

So, some code: