I present you a interesting mind challenge:
You have 12 coins. Eleven are made of gold; one is counterfeit. You don’t know which one because they all look alike. Also, you don’t know if the fake coin is heavier or lighter than a real gold coin. All eleven gold coins weigh the same.
You have a classic balance scale: two pans suspended from a pole with the center point balanced on a post. The scale can compare the weight of an object or objects in the left pan (L) with an object or objects in the right pan (R ). The scale will tell you if pan L is equal, heavier or lighter than pan R.
The answer, if is possible or not, will be published soon…
Meanwhile you can try to resolve the challenge … And raise your findings in the comments …
March 29th, 2008 at 12:13 am
Ok, I think it is possible, here’s I’d do it (I hope i’m right):
and if they were the same again, then it is the last one left (we can know if its hevier or not by weighing it with any gold one) if the 3 are different (hevier or lighter) then we take 2 of them and weight them agains each other.
First i’ll put 4 coins on each pan (8 coins) and observe. If both are the same weight, then the fake coin is in the 4 coins left. Put 3 of them agians 3 gold ones (from the
Now lets return to the case where the 4’s are not the same. we take 3 from the heavy pan and throw them away, take 3 from the light pan and put them in the heavy pan, and take 3 from the 4 gold coins and put them in the light pan, so that we are now weighing 4X4 again but with different coins.
If nothing changed, then it’s either one of the unmoved coins (can be known which). if they became the same weight, then its in the 3 we threw away (can be known which exactly like the way mentioned earlier) and finally if the balance switched, then it is in the 3 we moved from the light pan to the heavy pan (can be known which ).
I hope I haven’t missed anything!
May 2nd, 2008 at 3:35 am
Weighing#1: Take the twelve coins and divide in two stacks of six putting a stack of six on each side of the balance scale.
Weighing#2: Remove and set aside the six heaviest coins and then take the six coins from the lightest side of the scale and divide them into two stacks placing a stack of three on each side of the balance scale.
Weighing#3: Remove and set aside the three heaviest coins and then take the three coins from the lightest side of the scale and place 1 of the remaining 3 coins on each side of the scale
IF the two coins in the balance scale are equal, the remaining coin in hand is most likely the counterfeit, IF the two coins in the balance scale are unequal, the lightest coin on the scale is most likely the counterfeit. IF the counterfeit happened to be a heavier metal than gold (not likely) then the only way identify it absolutely would take at least 1 more weighing.
May 3rd, 2008 at 7:29 pm
are yaar pehle laa kar to do wo saaare coind fir batata hun ki kaun sa asli hai
May 28th, 2008 at 9:50 am
First number all the coins from 1 to 12.Then follow the 3 weighing steps:
1.Left:(4 8 10 11) right:(1 2 5 7)
2.Left:(2 4 7 12) right:(3 5 6 11)
3.Left:(5 6 10 12) right:(7 8 9 11)
Let variable count=0;
Weighing I: Add -1 with count if left pan down, +1 if left pan up.
Weighing II: Add -3 if left pan down, +3 if left pan up.
Weighing III: Add -9 if left pan down, +9 if left pan up.
Final value of count will be indicating the counterfeit one! Its appearance on lighter or heavier side will be indicating whether its light or heavy.
December 7th, 2008 at 11:57 pm
Very interesting site.
November 20th, 2009 at 11:31 am
Very interesting post!!!It is possible by weighting them individually by using electric weighting machine if it is allowed for measuring.
Great post on gold and silver coins. We will include some of your writing and link into our newsletter to our gold coin collector forum newsletter and social website.
gold coins
January 21st, 2010 at 7:33 am
Thanks for the information, we will add this story to our blog, as we have a audience in the gold sectors that loves reading like this. Thanking you. gold coins
August 28th, 2010 at 11:27 pm
Hi buddy, very informative post. Please keep them coming.
September 3rd, 2010 at 10:25 pm
Nice site, you know after 4 years of studies I guess I have to admit I was wrong about this. Thanks for opening my eyes!