1: chalk 6 1 box, of which 60 boxes have the same quality, and the other box is less than other boxes 1 piece. How many times can you find this box of chalk by weighing it with a balance?

At least once: 30-30 are placed at both ends of the balance, and the result is balanced, so the last box is. This is the luckiest:)

2. "Guarantee" means that even if you are unlucky, you can find it in these times and you don't need it anymore. This assumes that after each weighing, you have to prepare for the worst: you have to weigh it again.

This kind of problem needs to divide the object to be weighed into three parts and assume that the object is in the group to be weighed the most times.

If you weigh (20, 20, 2 1) for the first time and put two 20s on it, the result is balanced, and the one you are looking for is in the group of 2 1. (Because finding one in 2 1 won't take less time than finding one in 20-under the condition of ensuring finding it. )

The second call: (7, 7, 7), no matter which "7" it is, it needs to be called again;

The third weighing: (2, 2, 3)-Suppose what you are looking for is at 3, if it is at 2, it is not "at least guaranteed".

The fourth weighing: (1, 1, 1) can find out whether it is balanced.

In other words, at least four times, we can guarantee to find it for you. But if you ask for fewer times, you can't "guarantee".

Note that this kind of problem looks like dichotomy, but due to the special balance principle, the weighed object is actually divided into three parts (as equal as possible).

I hope you can understand.