Riddles: 10 Goldsmiths and 100 rings (Answer)

The king line the goldsmiths up on a row and numbers them 1 -10.

The king then takes one ring from goldsmith no. 1, two rings from goldsmith nr. 2, three rings from goldsmith no. 3 etc.

The king then weighs the rings, which are supposed to weigh 10 grams x ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) = 550 grams

If 1 gram is missing, then it is goldsmith no. 1 that has been cheating, as one of his 9 gram rings has been weighed.

If 2 grams are missing, then it is goldsmith no. 2 that has been cheating, as two of his 9 gram rings have been weighed.

If 3 grams are missing, then it is goldsmith no. 3 that has been cheating, as three of his 9 gram rings have been weighed.

etc.

This way, the king can determine exactly which goldsmith has cheated him.