Twenty-seven glass boxes have been stacked together to form a cube.
Some of the glass boxes have a gemstone inside. Image A shows a view of the cube from above, B shows a view from the side, and C shows a view from the front.
How many of the boxes contain gems?
UK Version
The cube below is made up of 27 clear plastic boxes.
After your friend fills some of the boxes with gems, you look at the cube from three different directions.
By comparing the gems you can see from the three viewpoints, A, B and C, can you work out how many gems there are in total?
Hints
Click a Tab to reveal the Hint.
If you try to consider the entire cube at once, you'll just end up in a muddle.
Try taking it one row at a time, starting from the view that shows the fewest gems for that particular row.
US Version
Views B and C look at the cube from the side. When working out how many gems there are in the topmost row, you only need to consider the top rows of these views. Try comparing them with view A.
In views B and C, there is one gem in the central column of each. These views can't contradict one another, so there can only be one gem, right in the center of the row. This corresponds with the central gem in view A.
UK Version
Views B and C look at the cube from the side. When working out how many gems there are in the topmost row, you only need to consider the top rows of these views.
In views B and C there is one gem in the central column of each. These views can't contradict one another, so there can only be one gem, right in the centre of the row. This also agrees with view A, which has a gem right in the centre.
For the second row from the top, you only need to consider the middle row of views B and C.
From view B you can see two gems, while for view C you can see one. For these views to agree, there can only be two gems. This doesn't contradict view A, either.
US Version
When working out how many gems are in the bottommost row, look at the bottom rows of views B and C.
In view C, two gems can be seen, but in view B, only one can. The only way views A, B, and C can agree is if there are two gems in this row.
How many are there in total?
UK Version
When working out how many gems are in the bottom row, look at the bottom rows of views B and C.
In view C, two gems can be seen, but in view B only one. The only way both views can agree is if there are two gems in this row.
So, how many are there in total?
Solution
Incorrect
Too bad!
US Version
If you're getting confused, try drawing it out and see if that helps.
UK Version
If it's getting too confusing, try drawing a diagram and thinking it through.
Correct
US Version
Correct!
Only five of the boxes contain gemstones. Less than it might seem at first, eh?
UK Version
Boxing clever!
Your friend filled five of the boxes with gems. Is that fewer than you expected?