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Two mathematical problems
1, in any case, it is impossible to put all seven cups down.

If the mouth of each cup is facing down, it will turn over odd times. The total number of seven cups to be turned is the sum of seven odd numbers, which is also odd numbers.

Turn it six times at a time, and turn it n times to be 6n.

6n is an even number, so you can't put everything down.

Two or three times

The first time: take five first, and you can determine which one is inside.

The second time: take two of the five lighter ones. If it is lighter than 1000kg, it is in it.

The third time: choose one of the two.