Coins Puzzle

talk random
1

Ok, my grandad gave me this brainteaser and I thought it was cool - see if you can get it.

You have 12 identical coins, but one is a different weight to the others. (maybe heavier, maybe lighter, you don’t know which) You also have a pair of scales (the balance type where you load stuff on each end and see if it balances) You are only allowed 3 ‘weighings’ to find out which coin is the odd one and whether it is heavier or lighter.

Me and my dad came up with an answer, but it seems really complex. :stuck_out_tongue:

Can you do it in 3 goes?

2

So if you got 2 scales to work with:

Divide the pile into goups of 4, so 3 groups, weigh 2 of them. If they weigh the same its the 3rd pile, otherwise its the different scale (heavier one I am going to have to go with) then you divide that pile in half. weigh em both, then divide agian, weigh again.

That only works if you know it is heavier or lighter though, thats a cool puzzle!

3

i don’t think you have 2 SETS of scales, you have a pair of scales, which i interpret as being one unit… is that correct?

and ben, when you say your answer is complex, is it still within 3 weighs (i.e legit)?

i think i’ve got a solution - and it works whether the coin is lighter or heavier :smiley:

4

Yeah - one ‘set’ of scales, sorry if that’s confusing. But you don’t need two scales anyway for your answer? But that would be an interesting problem in itself… :ponder:

My answer is still within 3 weighs, works when nit’s heavier or lighter, it’s legit, but it just seems really messy and hard to explain/do, whereas most of these things have a simpler “Why didn’t I think of that!” sort of answer, if you see what I mean :stuck_out_tongue:

We wrote out our answer to explain to my grandad - I’ll post it up when I can get it off my dad’s laptop. I’d be interested to see what you’ve got.

5

i got half of it:)
should i post the answer?
edit: post your answer. i dunno how to get which one is heavier/lighter

6

Yeah i worked it out for 3 weighings, pretty simple. Howd u get 2 weighings hybrid?? That dont seem possible. Ill have a bit more a of a think about it.

7

edited my post. it would work two weighings just to find the odd coin if you choose the right pile

8

you have to be able to work out which is lighter/heavier as well… its no use saying you can work it out if you ignore that part, because thats the whole point of the puzzle, to work it out WITH those parameters.

9

Hmm, yeah just realised my way doesnt work if u dont know if it is lighter or heavier. This requires more brain power, oy my brain hurts…

10

Here’s our answer.

Anyone else who’s got one that works - I’d be interested tosee, attach it or use a spoiler tag or something :wink:

11

wow that sure is long and complex…
seems to work, but it’s one of those things where if you DID make a logic mistake, it’d be hard to pick up.

so i ended up just doing a google search and found a site with teh answer, it’s the same kind of procedure as you did, but they numbered the coins and it made it a lot clearer. I think theirs actually WAS shorter too.

good job though, must’'ve taken a while.

12

Ahh - Numbering the coins would be a good idea, that ought to make it easier to explain at least.

13

0 weighs. Drop every coin to the ground. The odd one will have a different sound to it.

This makes the solution legit as you can do it without a single weigh and show a big middle finger to the question! :stuck_out_tongue:

14

nah, because they could argue that the difference in weight is so small that you wouldn’t hear a difference, nor could you tell if it was heavier or lighter.

my original solution was similar - just use your hands to weigh each coin and find the one that is different :stuck_out_tongue: but it’s not really valid i think.

15

Such a negligible weight difference would not be valid in the first place anyway :stuck_out_tongue: