Riddle Ye! The Real Solution
It’s rather elaborate.
The first one was close but no cigar. The other two were…interesting…but wrong.
1) #1 cuts off a third, and let’s say #2 decides to take it. But #3 thinks the third was too big. Hence #3 is unhappy.
2) Obviously kid C thinks all slices are equal. But what if B thinks the slice A took was too big?
3) This requires compromise which does not guarantee all three will be satisfied.This is how its done (let’s see if I can type it out after getting 5 hours sleep in the past ~50 hours)… NB: A person is satisfied (happy) when they think that they have received pieces equal to or bigger than everyone else. Noone has qualms about watching someone else take a slice they consider too small.
Person A cuts what he considers to be one third of the cake, and offers it to B. B either thinks it is too large (goto 1) or too small (goto 2).
(1) B cuts the third down to size as he sees fit, the remainder becoming part of the remaining 2 thirds. He then offers his third to C. C thinks it’s either too big (3) or too small (4).
(3) C takes the slice. Then, B thinks he has taken one that’s just fine, and A thinks it’s too small (leaving all the more for him). Then it remains to divide the remaining 2/3 of the cake between A and B – this can be done as per the method with 2 people. Hence, in this case the solution is complete. #
(4) C thinks the slice is too small, so he refuses and gives it back to B. B thinks the slice is the right size – he cut it. A thinks it’s too small – his original slice has had some amount removed from it. Hence B takes the slice, and all are happy. The remaining two thirds are divided as per the method for 2 people. Solution complete. #
(2) B thinks the slice is too small. He passes it straight on to C. C either thinks it’s too large (5) or too small (6).
(5) C thinks it’s too large. He takes it. A thinks the slice is just right – he cut it. B thinks it’s too small. All are happy. The remaining 2/3 are divided as per method with 2 people. Solution complete. #
(6) C thinks it’s too small. He passes it on to A. A originally cut this slice, so he thinks it’s fine. He takes it. B and C both thought it too small. B & C divide the remainder as per method with 2 people. Solution complete. #