[CV084] Which Boxes to Move?

084 - Which Boxes to Move?

Which Boxes to Move? is a puzzle in Professor Layton and the Curious Village.

Puzzle

In preparation for your big move, you've packed your belongings into 20 boxes and arranged them as shown below. With everything packed, you are now ready to label each box with its contents. In order to do so, though, you'll need to move a few boxes around.

How many of the boxes can't be labeled without rearranging the stacks?

Hints

Click a Tab to reveal the Hint.

Fourteen boxes are visible in the illustration. You have to use what you can see to visualize where the hidden boxes are.

You can clearly see all the boxes in the top two levels of the pile, so you only need to worry about the two layers of boxes closest to the ground.

The boxes are stacked upon each other, so any box not directly on the ground must have another box supporting it from below.

Knowing this, you can infer that there are no fewer than six boxes in the layer that's second from the bottom, and no fewer than nine boxes resting directly on the floor.

Working from the ground up, you can deduce there are nine boxes on the first layer, six boxes on the second layer, four boxes on the third layer, and then one box that rests on the entire stack. That gives you a total of 20 boxes, which is how many the puzzle says you have.

With all boxes accounted for, all you need to do is figure out which of these hidden boxes are completely surrounded by other boxes on all sides.

Solution

Incorrect

Too bad!

There are 20 boxes in total. Try to figure out how many boxes are on each level of the pile.

Correct

Quite right!

Moving down from the top level, you have one, four, six, and nine boxes. The only boxes you can't access without rearranging things are the three indicated in the above picture.

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