How many triangles are in this figure?

What's the minimum number of glasses you need move to change the top arrangement (full-full-full-empty-empty-empty) to the bottom one (full-empty-full-empty-full-empty)?

You're given a three-inch wooden cube and a saw. Cut the cube into 27 one-inch cubes. You can do it in six cuts, i.e. two cuts in each of three directions, but can you reduce the number of cuts by rearranging and stacking the pieces after each cut?

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You're given a three-inch wooden cube and a saw. Cut the cube into 27 one-inch cubes. You can do it in six cuts, i.e. two cuts in each of three directions, but can you reduce the number of cuts by rearranging and stacking the pieces after each cut?

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