Logic Puzzle: You Have Two Solid Lead Cubes. One Cube Is Slightly Larger Than The Other. A 'hole' or

Question

'tunnel' is cut through the slightly larger cube. The smaller solid lead cube can now be pushed through this opening in the larger cube. Yet, the weight of the larger cube (now with the opening) is still heavier than the weight of the slightly smaller cube. How is this possible?

Great observation, dansinger101! However, the cubes remain cubes and the corners of the cubes remain undisturbed...

tlbs101, I'm not sure what you mean. This puzzle does not specifically rely on the word 'slightly.' The puzzle could just as easily said "...one cube is a little larger..."

I now understand that the hole is not necessarily cut in the larger cube. A hole is simply created in one of the cubes, yet the larger cube still ends up weighing more than the small cube. Another thing; the portion cut from the cube is discarded; it's simply waste material...

Helmut, I appreciate your answer. However, I don't see from your answer what the solution to this puzzle is....

jimschem, so what would be the weights of both cubes before AND after the hole is cut?

Answer 1

It's true for any ratio of sides (edges) of the large cube to smaller cube > 1.3248

So "slightly" means 32.5% greater in this case.

.

Answer 2

If by slightly larger, you mean that the sides of the larger cube are more than cube root of 2 long than the volume of the larger cube would be more than double the volume of the smaller cube whose sides measure 1. A cube whose sides measure about 1.2599 would have a volume of 2, and a cube whose sides measure 1 would have a volume of 1. The larger cube would need to be slightly larger than cube root 2 on a side to create the situation you describe. Assuming you could create a tunnel that measured exactly 1 on a side, you would remove slightly more than 1 cubic unit from a cube whose sides were cube root 2 long. Exactly how much larger is as subjective as slightly.

Answer 3

You don't mention whether the smaller cube REMAINS a cube during the pushing process. Lead is an extremely malleable metal, and could easily be extruded to a very fine wire which would pass through a small hole in the larger cube, allowing the larger cube to remain heavier than the smaller (former) cube.

Answer 4

If the smaller cube has sides 1" long
then the larger cube sides 1.3247" long.

The hole going through the large cube
is not round but a 1" square.

Answer 5

My own technique is to easily concentration on a colour one after the different merely. i will admit, i've got no longer solved the cube yet, yet I have been given 2 colorings solved numerous situations. better of success and save attempting! you will get it! :)

Answer 6

s2^3 - s2s1^2 > s1^3
(s2/s1)^3 - s2/s1 > 1
Suppose
x^3 - x - 1 = 0
Then
x ≈ 1.324718
so s2/s1 > 1.324718
or
s2 is at least 32.5% greater than s1
which is a little more than "slightly"