7.4. There are 100 coins, 99 of which are genuine and weigh the same, and 1 is counterfeit and lighter than the others. Dmitry has a pair of balance scales without weights, which always show incorrect results (for example, if the left pan is heavier, they will show either balance or the right pan being heavier, but it is unknown which). Help Dmitry find 98 genuine coins.
# Solution:

Let's number the coins from 1 to 100. Weigh the first coin against the second. If the scales show equality, then one of them is fake, and all the other coins are genuine, and we have achieved the desired result. If the scales do not balance, assume the coin numbered 1 is heavier. Then the second coin is definitely genuine (otherwise, the scales would have shown the correct result). Set aside the second coin in the bag for genuine coins.

Re-number the remaining coins from 1 to 99, and repeat the process.

Either we will get one new genuine coin with each weighing, and after 98 weighings, we will have found 98 genuine coins, or at some point, the scales will show equality, and we will achieve the desired result.

Criteria: Algorithm only without justification - 1 point. Case of equality not considered in a similar solution, otherwise justified correctly - 5 points.