Reasoning · Grade 2-1 Stacking Cubes

Problem

Count cubes in a stacked solid

The reference is 5 cubes: an L of 3 on the floor with the back corner grown into a 3-tall column. Four other solids each claim to come from it by moving exactly one cube. Find the one that really does, and mark the cube that moved.
Your answer
How to solve
Strategy Visualize Spatial Relationships — This is a 3D mental-rotation task, so the main move is to picture each solid in space (tool 17), ideally by imagining real cubes you could pick up and restack (tool 10). The clinching test is simple bookkeeping: a single move keeps the cube count at 5, so I list each candidate's cube count and keep only the one that has 5 cubes AND matches the reference everywhere except one relocated cube (tool 2).
1STEP 1

Count the reference cubes

The reference is a 3-tall column plus two floor cubes: 5 cubes.

3 + 1 + 1 = 5
2STEP 2

Use the rule: a move keeps the count the same

A move keeps the count, so the answer must also be 5.

3STEP 3

Count each candidate and keep only the 5-cube one

Counting, only Candidate 2 has 5 — the rest fall short.

4, 5, { ＜ }5, { ＜ }5
4STEP 4

Check the single-move match for Candidate 2

Lifting the front-left floor cube onto the column takes it from 3 tall to 4.

5STEP 5

Circle the cube that moved

So the cube to mark is the top of the 4-tall column.

Answer
Candidate 2 — the top cube of the 4-tall column
A single move must keep the count at 5. The reference has 5 cubes; only Candidate 2 also has 5, while Candidates 1, 3, and 4 have fewer than 5 and are correctly ruled out. Candidate 2 differs from the reference by exactly one relocated cube (a floor cube lifted onto the top of the column), so it is consistent. The circled cube is the one cube whose position changed.
Takeaway

Moving one cube never changes the count, so first keep only the shape that still has 5 cubes - then find the single cube that hopped to a new spot!

  • Count the reference cubes
  • Use the rule: a move keeps the count the same
  • Count each candidate and keep only the 5-cube one
  • Check the single-move match for Candidate 2
  • Circle the cube that moved