You have twelve identical-looking coins, one of which is counterfeit. The counterfeit coin is either heavier or lighter than the rest. The only scale available is a simple balance. Using the scale only three times, find the counterfeit coin.
Given: Four pieces of cardboard. You are told that each one is either red or green on one side, and that each one has either a circle or square on the other side. They appear on the table as follows:
Which ones must you pick up and turn over in order to have sufficient information to answer the question: Does every red one have a square on the other side.
Draw four connected lines, without retracing your path, that pass through all the coins.
You have a 9x12-foot rug with an 8x1-foot hole in the middle. Cut the rug into two pieces (no more and no less) so that the two pieces can be sewn together to make a solid 10x10-foot rug.
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