A rack contains nine identical-looking weights ranging from 1 kg to 9 kg. Four of these weights were removed from rack and arranged side by side. One pair of side-by-side weights had a weight difference of 8 kg, while two pairs had a weight difference of 7 kg.
Which weights were removed from the rack, and how were they arranged?
UK Version
A rack contains nine identical-looking weights, ranging from 1 kg to 9 kg. Four of these weights were removed from the rack and arranged side by side. One pair of side-by-side weights had a weight difference of 8 kg, while two pairs had a weight difference of 7 kg.
Which weights were removed from the rack, and how were they arranged?
Hints
Click a Tab to reveal the Hint.
US Version
It may seem as if there isn't enough information to go on here, but that's not true. There are more than enough clues in the text of the puzzle. Once you realize what the puzzle is saying, you will be able to determine which weights need to go in the lineup.
UK Version
It may seem as if there isn't enough information to go on here, but that's not true. There are more than enough clues in the text of the puzzle. Once you realise what the puzzle is saying, you will be able to determine which weights need to go in the line-up.
US Version
There are two possible lineups that work. That is to say, there are only four weights that work, but two ways to line them up.
UK Version
There are two possible line-ups that work. That is to say, there are only four weights that work, but two ways to line them up.
US Version
What you must focus on is the 8 kg difference in the lineup. There is only one pairing that results in an 8 kg difference.
UK Version
What you must focus on is the 8 kg difference between two consecutive weights in the line-up. There is only one pairing that results in an 8 kg difference.
You can only get an 8 kg difference by placing the 1 kg weight next to each other. It's not possible to create two differences of 7 kg if the 1 kg weight or the 9 kg weight occupies the leftmost or rightmost position, so these weights must be in the middle. All you need to do is fill in the left and right spots with weights that are 7 kg heavier or lighter than the weights next to them.
Solution
Incorrect
US Version
Too bad!
Check your work to make sure you haven't made any miscalculations.
UK Version
Too bad.
Check your work and make sure you haven't made any miscalculations.
Correct
Excellent!
There are two possible answers: 8, 1, 9, 2 or 2, 9, 1, 8. The only way to get the 8 kg difference is to have the 1 kg and 9 kg weights next to each other.