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# This isn't Math!

## Question

Sometimes, I find, math students get obsessed with numbers. So an exercise that I often assign the class is a geometric measurement problem. I assign each student in the class an identical solid rectangular prism and a string (that is randomly cut so that no student is guaranteed the same size string but each string is longer than the biggest length of the prism). The students are then challenged to come up with a method without the use of pencil and paper to find the measurement of two opposing corners of the prism like in the picture below. Remember the rectangular prisms are solid so a direct link is impossible. The students may share supplies in order to complete this calculation.

What is the least amount of student supplies needed to complete this calculation?

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Place 4 prisms... 2 side to side on bottom and 2 above these. Now remove one of the top prisms and measure the end to end distance using the string.

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use the string and gravity?

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Can the students use a marker to mark the string?

If so, they could start one end of the string on one of the yellow corners and mark the string where it reaches the nearest corner. Once that is done, move the string from the yellow corner to the corner that was used to mark the string. The marked piece of string should be moved in the same direction and should now be located in the air "above" the block. If the remainder of the string is long enough, it can now be directly connected to the opposing yellow corner and measured. If it is not, one of their classmates could use their string to measure the distance.

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If only the blocks and strings are allowed to be used, 5 blocks could be arranged to allow the string to pass from the top yellow corner of the bottom block to the bottom yellow corner of the top block. One block would be used as a spacer sandwiched between the two blocks just outside the diagonal. The last two blocks would be used as guides to make sure the blocks are aligned on the x and y axes.

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If only the blocks and strings are allowed to be used, 5 blocks could be arranged to allow the string to pass from the top yellow corner of the bottom block to the bottom yellow corner of the top block. One block would be used as a spacer sandwiched between the two blocks just outside the diagonal. The last two blocks would be used as guides to make sure the blocks are aligned on the x and y axes.

no markers of any sort. you are on the right track with this solution but there is a more efficient (less material needed) solution

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3 blocks and one string

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essentially the removal of the 4th block in Dege's answer is equivalent to K-man's

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