So the king (a)   (give) a carefully weighed amount of gold to a goldsmith.

The goldsmith (a)   (produce) a beautiful crown.

However, the king was worried that the craftsman (a)   (not use) all the gold to make the crown.

Dishonest craftsmen often (a)   (mix) gold with silver, which was cheaper.

But the king could not find a way of proving that the man (a)   (do) this.

So he asked Archimedes to solve the problem. Archimedes (a)   (know) that gold and silver have different densities.

The problem was that nobody could calculate the mass of an object like a crown. While he (a)   (think) about this, he decided to go to the public baths to relax.

While he (a)   (climb) into the bath, he noticed some water on the floor.

The water (a)   (spill) over the side of the bath. It was then that he realized that he'd solved the problem by accident.

The total amount of water that (a)   (spill) must be the same as the volume of my body, he thought.

He (a)   (be able) use a piece of pure gold and calculate its volume, and then test the crown and see it it was the same.

According to the story, he (a)   (jump) straight out of the bath and ran down the street naked shouting 'Eureka!, I've found it!'

Finally, the goldsmith admitted that he (a)   (cheat) the king. He was obviously punished. Archimedes had discovered a principle of buoyancy!