Sudoku

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Someone has eaten the cake you made for your Mum’s birthday next week. Out of your three flatmates – Tom, Ellie and Matt – one always tells the truth, and two always lie when food disappears. Tom says ‘I didn’t eat your cake’, Ellie says ‘Matt ate your cake’ and Matt says ‘I didn’t eat your cake.’ So who did eat it?

Tom ate the cake. One of Tom and Matt must be telling the truth (because only one person ate the cake), which means that Ellie is one of the liars and Matt didn't eat the cake. Therefore Matt was telling the truth and Tom must be lying.

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