There are 10 barrels of gold coins. In that, some of the barrels contain
1 gram gold coins and some of the barrels contain 2 gram gold coins.
There is a weighing machine which is allowed to weigh only once.
Which of the barrels contain 2 gram coins?
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Take 1 coin from one barrel 2 from next .....hope you got it
take 1 coin from first barrel, 2 coins from second, 4 coins from third, 8; 16; 32; 64; 128; 256; 512. weight will be from 1023 to 2046 included. if the answer is more than (2046+1+1023)/2=1535 there is 2 gram coins in tenth barrel, if less there will be 1 gram coins. for example it was more, now we have answer from 1535 to 2046. if the answer is more than (2046+1+1535)/2=1791 there is 2 gram coins in ninth barrel, if less 1 gram coins and so on...
You don't need any weighting, just look into these barrels. The 2-gram one will have half the coins.
I don't understand this.... Do the barrels have the same value?
I think with the information given, It would be,
you could shake it and the 2 size of coins will sounds different. I think the bigger the coin the lower the frequency. Because they are both made of the same metal.
But other answers could be :
- you could look inside.
- you could use a ultrasound. to check through the barrel.
- you could ask the the one who place the barrels there.
- you could check if it is written on the barrel.
for the weighing machine :
it would depend on the quantity of coins in each barrel. if the barrels are the same weight because there is two times more coins of 1 gram in a barrel. The weighing machine is useless.
If there is different amount of coins in every barrel, also.
thanks.
The simplest solution would be to grab 4 or 5 coins from each barrel. Once each set of 4 or 5 coins has been removed compare them by placing separate sets in each hand. Compare 1&2, 3&4, ..., 9&10. Among the 5 comparisons, which set had felt unbalanced. From this set, choose the respective barrel which contained the heavier coin, this barrel is filled with 2 gram coins. This way you do not need the machine at all, it is important to consider your resources even if they are not explicitly stated in the question, ie- your hands.
The simplest solution would be to grab 4 or 5 coins from each barrel. Once each set of 4 or 5 coins has been removed compare them by placing separate sets in each hand. Compare 1&2, 3&4, ..., 9&10. Among the 5 comparisons, which set had felt unbalanced. From this set, choose the respective barrel which contained the heavier coin, this barrel is filled with 2 gram coins. This way you do not need the machine at all, it is important to consider your resources even if they are not explicitly stated in the question, ie- your hands.
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