4. Among 25 coins, two are counterfeit. There is a device into which two coins can be placed, and it will show how many of them are counterfeit. Can both counterfeit coins be identified in 13 tests.
4. Answer: Yes.

Solution: The first 11 trials, we place new coins in the device each time.

If we get an answer of "2" at least once, the goal is achieved.

If we get an answer of "1" twice, we place one coin from the suspicious pair and one genuine coin (such coins are identified by this point) in the device. This trial will identify one fake coin.

We do the same with the second suspicious pair.

Suppose the answer "1" was given once. This means that one fake coin is among two tested coins (A and B), and one is among three untested coins (C, D, E).

Twelfth trial: place A and C in the device.

Answer "2" - everything is clear.

Answer "1". Possible scenarios: fake coins (A, D), (A, E) or (B, C).

Test A and D. Each possible answer points to a specific pair.

Answer "0". Fake B and one of two - D or E. This is easily determined by placing D and a genuine coin in the device.

The last case: all 11 trials gave an answer of "zero." This means both fake coins are among the three remaining. They can be easily identified in two trials.

## Instructions for checking:

the solution must be read very carefully,

if at least one case is left unconsidered, no more than 2 points should be given.