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2010 Math Kangaroo

Problem 22

Problem 22 · 2010 Math Kangaroo Stretch
Spatial & Visual Reasoning paper-cuttingnet-folding

Lines are drawn on a piece of paper and some of the lines are numbered. The paper is cut along some of these lines and then folded as shown in the picture. What is the total of the numbers on the lines that were cut?

Figure for Math Kangaroo 2010 Problem 22
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Answer: D — 20
Show hints
Hint 1 of 2
A line is cut only if the fold could not bring its two sides together; uncut lines are the fold creases.
Still stuck? Show hint 2 →
Hint 2 of 2
Figure out which numbered lines stayed as folds, and add up the rest.
Show solution
Approach: separate fold creases from cut lines, then add the cut numbers
  1. Match the folded result to the flat sheet to see which lines were creases and which were cut.
  2. Add the numbers on the lines that were cut.
  3. That total is 20.
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