Lateral Thinking #19- Fair Share -
Five boys order a pizza together. When it arrives, they notice that it has not been cut.
Using nothing more than a knife (and ignoring the distribution of the pizza toppings), how can they go
about cutting and distributing the pizza such that each of them is satisfied that he has received at
least 1/5 of the pizza?
HINT: In order for there to be a consensus that a slice is fairly cut, each of the boys
will need to have an opportunity to adjust the size of the slice.
ANSWER:
Let's label the boys A, B, C, D, and E. A cuts a slice that he believes to
be 1/5 of the pizza. B then has the opportunity to reduce the size of the piece if he believes it to be
more than 1/5. If B believes the slice is 1/5 or less, he does not adjust its size. Then C, D, and E,
in turn, have the opportunity to do the same. The last person to "touch" the slice keeps it as his share.
If noone reduces the size of a piece of pizza, then the person that cut it keeps it as his share. The
remainder of the pizza (including any cut-off pieces) is then divided among the remaining four boys in
the same manner, then among three. The final division is made by one person cutting and the other
choosing
This solution (strategy) forces the person cutting the pizza not to cut it smaller than 1/5, because
otherwise there's a good chance they'll get stuck with it (and it will be their own fault). It's
not a perfect solution as the pizza slices will likely get a tiny bit smaller with each new piece given
out as people will tend to err on the side of caution when cutting the slice. But it's nearly perfect and
as close as can be achieved with just a knife.
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
