Answer: 3 diamonds.

Solution. From the condition of the problem, it follows that 9 diamonds and 1 emerald weigh as much as 4 emeralds. Thus, if we remove one emerald from each side of the scales, the equality will be preserved, that is, 9 diamonds weigh as much as 3 emeralds. This means that 3 diamonds weigh as much as 1 emerald.

## Criteria

1 p. The correct answer is obtained.

4 p. The correct answer and justification are present.

If the work mentions (or illustrates) three cases of balance on the scales:

- 9 diamonds and 1 emerald balance 4 emeralds,
- 9 diamonds balance 3 emeralds,
- 3 diamonds balance 1 emerald,

then this is considered a correct justification.
Problem 4. As is known, balance scales come to equilibrium when the weight on both pans is the same. On one pan, there are 9 identical diamonds, and on the other, 4 identical emeralds. If one more such emerald is added to the diamonds, the scales will be balanced. How many diamonds will balance one emerald? The answer needs to be justified.