You are in a cookie factory, and need to make a huge batch of chocolate chip cookies. The recipe calls for exactly 4 cups of sugar. Problem is that you have two buckets. One bucket holds 5 cups, the other 3 cups. Using these buckets, how can you measure exactly 4 cups of sugar?
Solution 1: Fill the 3-cup bucket and pour it into the 5-cup bucket. Fill the 3-cup bucket again, and pour it into the 5-cup bucket until the 5-cup bucket is full. That will leave exactly 1 cup of sugar in the 3-cup bucket. Dump out the 5-cup bucket, and dump the 1 cup from the 3-cup bucket into the empty 5-cup bucket. This leaves 1 cup in the 5-cup bucket. Now fill the 3-cup bucket again and add it to the 5-cup bucket. Now you have exactly 4 cups of sugar in the 5-cup bucket!
Solution 2: Fill the 5-cup bucket. Pour it into the 3-cup bucket. This leaves 2 cups in the 5-cup bucket. Dump out the 3-cup bucket. Now pour the 2 cups from the 5 cup into the 3 cup. Refill the 5 cup. Now pour the 5 cup into the 3 cup until the 3 cup is full. That will leave exactly 4 cups in the 5-cup bucket!
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