Counterfeit Coins: What is the smallest number of weighings necessary to determine which stack is bogus?
Counterfeit Coins: What is the smallest number of weighings necessary to determine which stack is bogus?
Counterfeit money: What is the smallest number of weighings required to determine that the battery is fake?
COUNTERFEITING parts are presented eleven piles of silver dollars, each consisting of ten pieces. A whole stack is false, but I do not know which. You know the weight of the dollar in real money and you've also said each piece of counterfeit weighs one gram more than expected. You can weigh coins money in a pointer scale (ie, a scale that gives the exact weight of what is placed above). What is the smallest number of weighings required to determine that the battery is fake?
You can do this while it weighs. Take 1 coin from the first pile, 2 parts of the second 3 rooms of the third, etc. Do not stack 11. This will give you 55 coins. If the reading is correct (expected weight) to all 55 who I said that this battery 11 to counterfeiting. Otherwise, the difference in reading indicates that you must stack #. If the reading is off by 1g, which states that you stack 1 Counterfeiting of money (because it took "a" piece of the stack). If the reading is more than 2 g, the stack 2 to counterfeiting. etc Answer: A weight. Take 1, 2, 3, ... , 10 units, respectively, the top ten.
femtorgon2
September 4th, 2009 at 2:47 am
1 weighing.
Weight a group of:
0 from stack 1
1 from stack 2
2 from stack 3
3 from stack 4
etc.
up to all 10 from stack 11
This way, when you weight the whole bunch, if it weighs the correct amount, you know stack 1 was counterfeit. If it weighs 1g too much, stack 2 is counterfeit. 2g too much, stack 3 is counterfeit, etc. to 10g too much, then stack 11 is counterfeit.
Puzzling
September 6th, 2009 at 4:09 pm
You can do this all in one weighing.
Take 1 coin from the first pile, 2 coins from the second, 3 coins from the third, etc. Don’t take any from the 11th pile.
That will give you 55 coins.
If the reading is accurate (the expected weight) for all 55, that tells you that pile 11 has the counterfeit coins. Otherwise the difference from the expected reading tells you the pile #.
If the reading is off by 1g, that tells you that pile 1 has the counterfeit coins (since you took *one* coin from that pile).
If the reading is 2g over, pile 2 has the counterfeit coins.
etc.
Answer:
One weighing.
Take 1, 2, 3, … , 10 coins respectively from the first ten piles.
Awms A
September 8th, 2009 at 7:40 am
One weighing.
Label the stacks 0 through 10. Then take k coins from stack k, for each k. Weigh all of those coins (although you may want to keep them separate so that you can put them back in their stacks when you’re finished).
Take 55x the weight of the genuine dollar and subtract it from the weight you get. However many grams are left is the number of the counterfeit stack.