View Full Version : Find the Coin
05-31-2009, 10:03 PM
9 coins, one is lighter than others.
use a balance (no poise) twice only to find it.
06-01-2009, 12:45 AM
Divide the coins into three groups, labeled 1 through 3.
Compare group 1 with group 2. If they are the same weight, the light coin is in group 3. If they are different, the light coin is in the light group, either 1 or 2.
Divide the light group into three. Compare one coin to another; if they are the same, the light coin is the remainder. If they are not the same, you know which is lighter.
06-02-2009, 01:02 AM
I have a feeling Janey left us, but I'll take a crack at it.
Speaking of crack, this sounds like something from the dope salesman's exam. :laugh:
Three weighs is as close as I could get:
From the nine coins, place one random coin in your hand; place four coins on each side of the beam; if the beam balances, you got lucky, the light coin is in your hand. If the beam tips, the light coin is one of the four on the high side.
Next, pull one coin off of each side, if the beam now balances the light coin was pulled from high side. You did it - with just two weighs.
If the beam did not balance, one of the three coins on the high side is light.
Take the three coins from the high side and weigh again to find the light one. One coin on each side of the beam and the remaining coin in your hand. If the beam now balances the light coin is in your hand, otherwise the light coin is on the high side.
I can't think of a sure way to get it with just two weighs.
06-02-2009, 02:24 AM
Pfiffle, balderdash, and plain ol' hooey. Y'all are way outta my league:p:p:jester:
And a generous dab of H SH$$ thrown in:dizzy::dizzy:
I'M LUCKY TO WAKE UP ON THE RIGHT SIDE OF THE BED!!!!:D
Pick any coin and drill a hole in it. It is now the light coin and throw the scale away! :laugh:
06-02-2009, 06:05 PM
It hit me today. :laugh:
New plan - Place three coins on each side of the scale, hold three coins in your hand.
If the beam balances, the light coin is among the three coins in your hand. If the beam tips, the light coin is one of the three on the high side.
Place two of the three coins on the scale... you know the drill.
06-02-2009, 08:23 PM
As I typed my first post here, I simplified my explanation above and left out the word equal in the first sentence, but my way works with two 'balancings'.
Restated, make three groups
: 1). A, B, C
2). D, E, F
3). G, H, I
"Weigh' or balence any two groups.
This first 'weighing' tells you which group it's in. Either the light group shows up on the balance, or it's the extra group.
Using the same principle above, the second 'weighing' of the light group thus shows which coin within this group is lighter. Divide the light group as above; 'weigh' any two of the coins, setting the third aside. Either the light coin...
Maybe the OP didn't realize it was so easy and wanted to show off the solution??
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