Coin weighing problem

Q1: Now there are 9 coins, one is lighter than the other 8, give a no weight balance, at least a few times can be weighed light coins??

A1: The dichotomy can be used, but here is the three-point method is better.

Q2: Following Q1, if there are 10 coins? 12 of them? 100 of them? What about n?

A2: first three points, in the narrow three-point range.

Q3:9 a coin, there is one and the other 8 different weight, but do not know is more than the other 8 light or heavy, ask several times can be weighed out this coin?? The total number of coins is 10? 11 of them? What about n?

A3:

Q4:9 coins, the first pile of 3 standard weights, the second pile 3 lighter than the standard weight, the third pile of 3 than the standard weight, several times to distinguish the three coins? There are 4 of them in each heap? 5 of them?

A4:

Q5: Ten piles of coins, each pile of 10, each pile of 10 coins are the same weight (weight known), which has a pile of coins than the other light, give you a scale of the weighing, how to only say once to know the lightest pile of coins??

A5: The first heap takes 1, the second heap takes 2, the third heap takes 3, ... and the tenth heap takes 10, and all the coins are taken out into piles, and then the scales are weighed.

Coin weighing problem