Share the Love
I've got a new puzzle for you. Since we have such a large family, we can all relate with having to share. The worst time for this though, is around Easter and Halloween when you've got all that great candy. Being highly intelligent individuals, though, we want to be efficient with our sharing so that we can get on with eating our own candy. After all...after me, I like you best, right?
Suppose that you got a 5 by 8 piece of chocolate for your enjoyment, but your parents say you have to share it.....with everyone in the family. Okay, not everyone in the family, but you do have to divide into 40 pieces. What's the fewest number of cuts that you need to make to produce the 40 pieces? For bonus points and enduring admiration from this Aggie, prove your answer.
By the way, you can only cut the chocolote in straight lines (horizontal or vertical; no diagonals), and you cannot stack pieces.
10
comments from:
Melissa,
Michael,
Melissa,
Michael,
Patti,
Michael,
Michael,
Caci,
Caci,
Michael,
10 Comments:
question:
when you say they cannot be "stacked" does that mean directly on top of each other? could they be cut simultaneously while lying "next" to each other?
Stacked would mean directly on top of each other. They may be cut while lying next to each other.
i think i have the answer. should I email it to you or post it here?
Go ahead and email it to me and I'll post whether you are correct or not.
I can divide it equally by 40 without cutting it at all, so is it part of the puzzle that you must actually cut it?
Yes, you must actually cut it into pieces.
Aunt Patti has a great answer for this puzzle, but it also caused me to realize that the puzzle is poorly worded from the source that I used and that my earlier comment to Melissa did not make it any better. Please see this quick excerpt from my response to Aunt Patti:
"For extra fun tell me how many distinct times the knife actually cuts a piece of chocolate. So, where you have a 3rd cut going through two pieces we would now count that as the 3rd and 4th since the knife is making two separate 'cuts' for each piece of chocolate."
yes we are finding poorly worded problems aren't we?
so, get back with me on my answer because now you seem to have changed my way of thinking. I thought if it was cutting a horizontal line, even if 6 pieces came out of it, it was one cut, but you seem to be saying that is 6 cuts. Am I reading you correctly?
I emailed you with an answer never to hear from you again....what is the correct number of cuts????
Sorry. I forgot to post on this. Aunt Patti figured a way to do this with 6 cuts and if you define cut as a single slice of the knife, then I think her answer is probably the best. Perhaps she'll post the technique her for us to see.
The answer that's provided with the puzzle is 39. When a cut is defined as the knife going through a distinct piece of chocolate, that is the only answer that is possible. One cut of the knife will make two pieces. Another cut gives you three. Another cut gives you four. So your proof is by induction and you know that to get n pieces will require n-1 cuts.
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