Table of Contents

- 1 Can you find the counterfeit coin using just two weighings?
- 2 How much does a fake coin weigh?
- 3 How many weighing Do you need to find the counterfeit coin among 81 coins?
- 4 How can you tell a fake coin?
- 5 How do you determine which bag has fake gold?
- 6 How much does a counterfeit 10 Gramme coin weigh?
- 7 How many stacks of 10 coins are on a scale?

## Can you find the counterfeit coin using just two weighings?

Solution 1 Take any two of them and put them on the opposite cups of the scale. If they weigh the same, it is the third coin in the lighter group that is fake; if they do not weigh the same, the lighter one is the fake. Thus the problem is solvable in two weighings.

**What is the minimum number of weighings needed to find the fake coin?**

two weighings

By the way, two weighings is the smallest number of weighings that guar- antee finding the fake coin.

### How much does a fake coin weigh?

The fake coins weigh exactly 1 ounce each, while the real gold coins weigh 1.01 ounces. There is a large scale with enough room for all the sacks in the vault, but as soon as you weigh something it will trigger an alarm, so you can use the scale just once before you must flee the vault.

**How can you tell if a coin is counterfeit?**

Use a scale that is accurate to within 0.01 grams to measure the weight of the coin. Compare your results to that of the genuine coin. If they are significantly off, you may have a counterfeit coin. Use an extremely strong magnet to see if the coin is attracted to it.

## How many weighing Do you need to find the counterfeit coin among 81 coins?

four weighings

It then takes only one more move to identify the light coin from within that lighter stack. So in two weighings, we can find a single light coin from a set of 3 × 3 = 9. By extension, it would take only three weighings to find the odd light coin among 27 coins, and four weighings to find it from 81 coins.

**What is the meaning of counterfeit goods?**

Counterfeit products are fakes or unauthorized replicas of the real product. Counterfeit products are often produced with the intent to take advantage of the superior value of the imitated product.

### How can you tell a fake coin?

Use a high precision caliper to measure the diameter and thickness of the coin. Use a scale that is accurate to within 0.01 grams to measure the weight of the coin. Compare your results to that of the genuine coin. If they are significantly off, you may have a counterfeit coin.

**How much do fake silver coins weigh?**

Counterfeit pieces range anywhere from 28 grams to 35 grams. Any piece weighing less than 31.10 grams is immediately questionable. Any piece weighing significantly more than 31.10 grams should also be questioned.

## How do you determine which bag has fake gold?

Explanation: Take one gold piece from the first bag, two from the second bag, three from the third bag, four from the fourth bag, and five from the fifth bag. If the weight on the scale ends in . 1, then you know the first bag has the fake gold. If the weight on the scale ends in .

**How can you tell a counterfeit?**

8 Ways to Spot Counterfeit Money

- Color-shifting Ink.
- Watermark.
- Blurry Borders, Printing, or Text.
- Raised Printing.
- Security Thread with Microprinting.
- Ultraviolet Glow.
- Red and Blue Threads.
- Serial Numbers.

### How much does a counterfeit 10 Gramme coin weigh?

All of the coins in one of these stacks are counterfeit, all the other coins are not. A real coin weighs 10 grammes. A counterfeit coin weighs 11 grammes. You have a modern scale that provides an accurate readout.

**How can you tell if a coin is a counterfeit?**

For some given n > 1, there are (3^ n – 3)/2 coins, 1 of which is counterfeit. The counterfeit weigh less or more than the other coins. Can you state on forhand (that is without performing any weighting yet) n weighting experiments with a balance scale, with which you determine the counterfeit coin, and tell if it is heavier or lighter?

## How many stacks of 10 coins are on a scale?

Lets say we place them all on the scale, for our one and only weighing, and it reads 553g. The only possible way this could have happened is if we placed 3 counterfeit coins on the balance, and that means that pile #3 is counterfeit. 11 Stacks of 10 Coins In every practical sense you do the same thing as before.

**Can you add 3 coins to the weighings?**

So, again we can add 3 coins, resulting in the weighings: The dots of the first 3 three weighings are filled in using the weighings for n = 3 (where coin c is replaced by 3 c -2, 3 c -1 and 3 c ). Notice that we have placed 37 and 38 according to the patrons `l r r’ and `r l l’ respectively.