Solve 8 Coin Riddle with 2 Weighings

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In summary, you are given eight coins of the same denomination, one of which is slightly heavier than the rest. Using a beam balance, you must separate out the heavier coin in only two uses of the balance. This can also be done with 9 coins or in general, with 3n coins if you can use the balance n times."
  • #1
mia5
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You are given eight coins of same denomination, out of the eight coins one coin is very very slightly heavy than the remaining seven such that you cannot separate it by weighing it in your palms. You are given a beam balance with the help of which you have to separate out the very slightly heavy coin but you are allowed to use the balance only twice.
 
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  • #2
There's probably a better way to word this but here is my solution.

Put 3 on one side, 3 on the other. If the scale doesn't tip, weigh the 2 that were not on the scale.

If one of the 3 tips, pick 2 of those and put them on the scale, if it balances it's the 3rd one of that group if not the scale will tip.
 
  • #3
Charmar said:
There's probably a better way to word this but here is my solution.

Put 3 on one side, 3 on the other. If the scale doesn't tip, weigh the 2 that were not on the scale.

If one of the 3 tips, pick 2 of those and put them on the scale, if it balances it's the 3rd one of that group if not the scale will tip.

absolutely correct :approve:
 
  • #4
You can do the same with 9 coins.
Or, in general, with 3n coins if you can use the balance n times.
 
  • #5


To solve this riddle, we can divide the eight coins into three groups of three, three, and two coins. Weigh the first two groups of three coins against each other. If the weights are equal, then the slightly heavy coin is in the remaining two coins. Weigh one of these two coins against a known good coin. If they balance, then the remaining coin is the slightly heavy one. If they do not balance, then the slightly heavy coin is the one on the scale.

If the first weighing of the two groups of three coins shows that one group is heavier than the other, then the slightly heavy coin must be in that group. Take two coins from the heavier group and weigh them against each other. If they balance, then the remaining coin is the slightly heavy one. If they do not balance, then the heavier coin is the slightly heavy one.

In both scenarios, we have successfully identified the slightly heavy coin using only two weighings. This method works because we are using the beam balance to compare the weights of the coins against each other, rather than measuring their absolute weight. By dividing the coins into different groups and comparing their weights against each other, we are able to narrow down the search for the slightly heavy coin in just two steps.
 

Related to Solve 8 Coin Riddle with 2 Weighings

What is the "8 Coin Riddle"?

The "8 Coin Riddle" is a mathematical puzzle that involves determining the weight of a fake coin among 8 identical coins using only 2 weighings on a balance scale.

How does the "8 Coin Riddle" work?

The "8 Coin Riddle" can be solved by dividing the 8 coins into 3 groups of 3, 3, and 2 coins. The first weighing is done with the groups of 3 coins on each side of the balance scale. If the scale is balanced, the fake coin is in the group of 2 coins. If the scale is not balanced, the fake coin is in the lighter group of 3 coins. The second weighing is then done with the 2 remaining coins from the lighter group, with one coin on each side of the scale. The heavier coin is the fake coin.

Is it possible to solve the "8 Coin Riddle" with fewer than 2 weighings?

No, it is not possible to solve the "8 Coin Riddle" with fewer than 2 weighings. The puzzle is specifically designed to be solved with 2 weighings.

What is the significance of solving the "8 Coin Riddle"?

The "8 Coin Riddle" is a classic problem in mathematics that tests logical thinking and problem-solving skills. It is also often used as a brain teaser or icebreaker in educational settings.

Are there other versions of the "8 Coin Riddle" with different numbers of coins and weighings?

Yes, there are other versions of the "8 Coin Riddle" that involve different numbers of coins and weighings. Some variations may have more or fewer coins, while others may allow for more weighings. However, the basic concept remains the same - to determine the weight of a fake coin using a limited number of weighings.

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