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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:04 am
(August 14, 2016 at 9:01 am)Anomalocaris Wrote: Does it involve shaving off frosting and portioning the cake and frosting separately?
Oy vey! Another good question. I've gotten rusty. But I'm going to say that gets resolved by the "using the minimum number of straight cuts possible" requirement. So, since it is possible to leave the frosting intact, the minimum number of slices won't allow you that maneuver.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:18 am
Hmmm, how about 10 cuts.
Step 1: 2 cuts to shave off the frosting from two opposite sides of the cake.
Step 2: 4 cuts through the cake parallel to the first two cuts to divide the cake, the frosting on top, and the fronting on the other two sides of the cake into 5 equal portions.
Step 3: 4 more cuts to divide the frosting removed in step 1 into 5 equal portions.
That seems like too many cuts for an elegant solution, but is the best I have at the moment.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:21 am
(This post was last modified: August 14, 2016 at 9:21 am by Whateverist.)
Actually, as I think about it, my stepson was two or three years into high school math when he showed me this problem. It only became a middle school math problem when I started giving it out to advanced sections of 8th graders - greatly simplified. I always gave the problem straight to begin with but would then give them a written statement of the problem with a good deal of structure added. Here is a hint by way of the simplified structure I would provide.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:27 am
My solution still works even if the frosting is thin and painted on. I just don't think it is the minimum cut solution.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:27 am
(August 14, 2016 at 9:18 am)Anomalocaris Wrote: Hmmm, how about 10 cuts.
Step 1: 2 cuts to shave off the frosting from two opposite sides of the cake.
Step 2: 4 cuts through the cake parallel to the first two cuts to divide the cake, the frosting on top, and the fronting on the other two sides of the cake into 5 equal portions.
Step 3: 4 more cuts to divide the frosting removed in step 1 into 5 equal portions.
That seems like too many cuts for an elegant solution, but is the best I have at the moment.
I see. So you don't need to remove the frosting from two of the opposite sides in Step1 since you'd leave an equal amount for each of the five pieces anyway. Then in Step 3 you could line up the top bit of frosting and the two side bits to make a rectangle the same width as the top square of frosting by a length of that increased by the two side bits.
The actual minimum number of total cuts needed is
.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:28 am
(This post was last modified: August 14, 2016 at 9:30 am by Whateverist.)
(August 14, 2016 at 9:27 am)Anomalocaris Wrote: My solution still works even if the frosting is thin and painted on. I just don't think it is the minimum cut solution.
Agreed, but the thought of its unspecified thickness seems to bother some.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:29 am
(This post was last modified: August 14, 2016 at 9:30 am by brewer.)
6 cuts. Didn't say that she had to serve all of the cake.
If all of the cake is to be served, 10 cuts.
I don't have an anger problem, I have an idiot problem.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:36 am
Yeah, this one is harder than the other one, for sure. Don't have the time right now to think about it, but if nobody else solves it within the next few hours, I'll give this a go later.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:40 am
(This post was last modified: August 14, 2016 at 9:47 am by Whateverist.)
(August 14, 2016 at 9:29 am)mh.brewer Wrote: 6 cuts. Didn't say that she had to serve all of the cake.
If all of the cake is to be served, 10 cuts.
Your'e right. I didn't make that clear initially so I went back and revised it while you weren't looking.
How big a piece were you thinking of giving each of us? Would the shape of each piece be the same? I can also do it in 6 cuts without serving up all the cake (while also making the pieces any size you like from tiny up to 1/8 of the cake each). I wonder if we used the six cuts the same way. Come to think of it, if I cut the entire cake into 8 equal pieces this way, I can do it with just 4 cuts.
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RE: Can you cut a cake fairly to solve this middle school math problem?
August 14, 2016 at 9:45 am
(August 14, 2016 at 9:36 am)Irrational Wrote: Yeah, this one is harder than the other one, for sure. Don't have the time right now to think about it, but if nobody else solves it within the next few hours, I'll give this a go later.
Maybe we should give our solutions under hide tags so that anyone can still do the problem themselves first if they want?
I'll give my stepson's solution under hide tags after someone else gives the solution, though I expect they'll be the same. But we're driving to L.A. early tomorrow so I'll give it tonight if it doesn't fall sooner.
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