It's raining and it's time

[Greg Ward]

When it's raining, too cold to glue and too wet in the shed and the timber outside is mouldy, it's time.

Mr.Swan has promised to balance the Budget and is thinking about using some iron pyrites to assist, but Malcolm has found out and wants to check his future fund investment.

There are 10 stacks of gold coins, each individual coin worth $10,000, each stack containing 10 coins. The coins are identical in size and appearance
One entire stack is counterfeit, but you don't know which one.
You know the weight of each genuine coin and you know the counterfeit coins are 10g heavier.
You can weigh the coins as you wish on an electronic scale.

What is the smallest number of weighings necessary to determine which stack is counterfeit?

Greg

[Ironwood]

I can see how to do it in 7 weighings.

But you could be lucky and do it in 2 if you pick the counterfeit pile in your 1st or 2nd weigh.

[ajw]

Maximum of 5 weighs for my method:

1. Weigh first 5 stacks in one go = x grams
2. Weigh second 5 stacks in one go = y grams

One group will be heavier, and can then calculate the average weight of a "real" stack.

3. Divide heavier 5 stack into 2 groups: 2 stacks in one group, 3 in the other.
4. Weigh first stack of 2. If this equals 2 "real" stacks, heavier fake stack must be in other 3. If not equal to 2 "real" stacks, weigh each of the two stacks to find the fake.

5. Weigh any two of the 3 in the remaining group. If this equals 2 "real" stacks, fake is the other stack. If not, weigh either of the two to find which equals the "real" weight.

ajw

[_fly_]

Answer 3. 5 and 5 to find heavier side. Then 2 and 2, if even weight, its the fake left off the scales. If its one of the 2 sides, split that up to find heavier side. 9 piles you can do in 2 weighings.

[Greg Ward]

Not there yet....
Greg

[_fly_]

Rethink tells me its ONE weighing. One from first pile. 2 from second and so on. If you know the weight of one coin. Thats 55 coins in total. The amount that its over tells you which pile. If its over weight by 30 grams it pile 3. I knew I was a programmer for a reason.

[Greg Ward]

Well done. Easy when you think about it.

Greg

[_fly_]

And I hated being wrong the first time. I would have sat up all night working it out.

[Greg Ward]

OK. Time for a 'high school' maths problem. But I'll start a new thread.
Greg

[andrewr79]

I still want that wood paneled 'like' button so I can give Fly some credit...clever thinking :)