Steve’s Chestful Challenge

At a glance

• Part 1: The chest and the solid cube each contain 1,728 cobblestone blocks. Steve is correct.
• Part 2: The hollow vault uses 728 blocks, leaving 1,000 blocks.
• Part 3: The leftovers make 15 full stacks with 40 extra blocks.

1. Prove the two models match

Page 1: chest total

A single chest has 27 slots, and every full stack contains 64 cobblestone:

27 ×64 =1,728.

Page 2: cube volume

The claimed solid cube has volume

12 ×12 ×12 =1,728 cubic blocks.

The totals match, so Steve’s claim is correct.

The side length also follows directly from the arrangement. Each stack-cube is 4 blocks long, 4 blocks wide, and 4 blocks high. Steve places 3 stack-cubes along each direction, so each side of the large cube is 3 ×4 =12 blocks. The full array contains 3 ×3 ×3 =27 stack-cubes, with no gaps and no blocks left over.

2. Build the hollow vault

The outside volume is

12 ×12 ×12 =1,728 blocks.

Because the walls are 1 block thick on opposite sides, the empty inside measures 12 −2 =10 blocks in every direction. Its volume is

10 ×10 ×10 =1,000 blocks.

The vault’s cobblestone shell uses

1,728 −1,000 =728 blocks.

Starting from the 1,728-block chestful leaves

1,728 −728 =1,000 blocks.

3. Restack the leftovers

1,000 ÷64 =15 remainder 40.

So the leftovers make 15 full stacks and 40 extra blocks.

Check

• 27 ×64 =1,728 and 123 =1,728.
• 728 +1,000 =1,728, so the shell and empty inside reconstruct the outer cube.
• 15 ×64 +40 =1,000, so the stack-and-remainder result reconstructs the leftovers.

Common errors

• Treating 27 as a one-dimensional row instead of 3 ×3 ×3 stack-cubes.
• Multiplying 27 ×4 for the large cube’s side length. Only 3 stack-cubes lie along each direction, so the side length is 3 ×4.
• Subtracting only 1 from 12 for the inside dimension. A one-block wall is removed from both ends of each dimension, giving 12 −2 =10.
• Reporting 15 remainder 40 without naming 15 full stacks and 40 extra blocks.