Question

Как узнать где фальшивая монета за 3 взвешивания

Answer 1

Для удобства пронумеруем монеты от 1 до 12.

Первым взвешиванием сравним две группы по четыре монеты: 1, 2, 3, 4 и 5, 6, 7, 8.

Answer 2

How to Determine a Fake Coin in 3 Weighings

Determining whether a coin is fake or genuine can be a challenging task, but it is possible to do so using a balance scale and three weighings. Here's a step-by-step guide on how to accomplish this:

1. Divide the coins into three groups: Start by dividing the coins into three equal groups, with each group containing an equal number of coins. For example, if you have 27 coins, you would have 9 coins in each group.

2. Weigh two of the groups: Take any two groups and place them on the balance scale. If the scale tips to one side, you know that the fake coin is in the heavier group. If the scale remains balanced, the fake coin is in the third group that was not weighed.

3. Weigh one of the groups from step 2: Take the group that contains the fake coin (either the heavier group or the unweighed group) and divide it into three equal subgroups. Place any two of these subgroups on the balance scale.

- If the scale tips to one side, you know that the fake coin is in the heavier subgroup. - If the scale remains balanced, the fake coin is in the third subgroup that was not weighed.

4. Weigh one of the subgroups from step 3: Take the subgroup that contains the fake coin (either the heavier subgroup or the unweighed subgroup) and divide it into three equal sub-subgroups. Place any two of these sub-subgroups on the balance scale.

- If the scale tips to one side, you know that the fake coin is in the heavier sub-subgroup. - If the scale remains balanced, the fake coin is in the third sub-subgroup that was not weighed.

By following these steps, you can determine the fake coin using only three weighings. It's important to note that this method assumes that the fake coin is either lighter or heavier than the genuine coins. If the fake coin has a different density, this method may not be effective.

Please note that the search results did not provide specific information on this exact method, but the steps outlined above are a commonly used approach for determining a fake coin in three weighings.