Grades 5-6 Video Solutions 2026-2026_5-6

Video Transcription

Video Summary

Ira wrote the numbers from 1 to 16 into the cells of a strip of paper as shown. Then she folded the strip in half as shown. She continued folding it in half in the same way and ended up with only two cells. Ira then poked a needle through the whole strip where the number 1 was written, unfolded the strip, and added up all numbers in the cells with a hole in them. What answer did she get? Okay, so when we fold this strip in half you can imagine that our 16 would be folded under our 1, 15 under 2, 14 under 3, and so on. Essentially we have these pairs of 17 you might notice. And then if we fold this once more our 8 is sort of gonna get folded under 1 and we'll end up with something that looks like this where we have 1 with the 16 and then the 8 and 9 under it as well. And similarly we're gonna have, since we're folding right here, our 5 and 12 would end up under our 4. So we have 4, 13, 5, and 12 here. Folding this in half once more you can imagine our 4 would, everything under 4 would also end up under everything under 1. So we have these four pairs of 17 that end up under our 1. So 17 times 4 we get 68.

Keywords

paper folding

number strip

hole punching

cell sum

combinatorics