This puzzle is not even close to easy. If you don’t get it at all look at Nine coins. You will need to combine for a while so if you don’t feel like it you should rather pick a different brain teaser.

# Thirteen coins

There are 13 exactly same looking coins. One of them has slightly different weight than the others – we don’t know if it is heavier or lighter. Can you tell in 3 scalings which one it is using even arm balance?

If this riddle by any chance seemed too easy for you, try 40 coins in 4 scalings – the principal is the same.

## Hint

You can move a coin between the scales you can take it off. You can even weigh the coins about which you already know they are not different. Try to combine...

## Answer

8 coins on scales (four and four), 5 aside.

1. Scales are balanced – coin is on the table.

2. Scales are not balanced – coin is on the scales.

Ad 1. Take 3 coins from the table and put them on one scale. Put three already checked coins on the other scale.

1.a Scales are still balanced – it is one of the two you haven’t scaled yet.

1.b Scales are not balanced – it is one of the three being scaled for the first time.

Ad 2. The different coin is among 8 coins already scaled. Take any two coins off the even arm balance and move any three coins from one scale to the other one. For the scaling to have sense you need to add checked coins (the ones from the table) so that there is the same number of coins on both scales.

2.a Scales are balanced – its one of the coins taken off the balance before this scaling.

2.b The different side than before goes down – its one of the three you moved.

2.c Scales stay the same as they were after last scaling – it is one of the three you didn’t move.

Ad 1a + 2.a You know its one of two coins. Compare one of them with a checked one – scales stay balanced or not.

Ad 1.b + 2.b + 2.c You know its one of three coins. They are now on the balance which is tipped to one side. Move one of the coins to the other scale leave one where it is and take off the third one. Add checked ones so that there is the same number of coins on scales. Balance either tips over to the other side it becomes balanced or it stays the same...