It is harder to describe than to demonstrate. Make a square with four of the picks. Then lay one pick so it bisects a side and only reaches the center of the square. Place a second pick so it touches this pick inside the square and bisects an adjacent side. You've made a small square in side the first square. Last use the last two picks to make a square with those two picks. This should give you two large squares that are 1 by 1 and a third square that is 0.5 by 0.5.
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Using 8 of the toothpicks, make a square with two on each side. Using another two, make a smaller square in one corner of the first. Using the remaining two, make a cross in the middle of the second square. One large square on the outside, one medium square inside it and four small squares formed inside that, for a total of six.
There is a pattern here: Level 1 uses 3 = 3 × 1 toothpicks Level 2 uses 6 = 3 × 2 toothpicks Level 3 uses 9 = 3 × 3 toothpicks So it looks like each level uses 3 times the level number of toothpicks. ı→ 3 × level = 24 → level = 24 ÷ 3 = 8 So Level 8 uses 24 toothpicks.
make a circle
Divde
3 is greater than the square root of 8.