AFOQT - Air Force Officer Qualifying Block Counting Spatial Apperception Questions and Answers 1 — Questions and Answers
Question 1: Imagine a single stack of 4 blocks, labeled A, B, C, and D from bottom to top. A second stack of 2 blocks, labeled E and F from bottom to top, is placed directly to the right of the first stack, with block E touching block A and block F touching block B. How many blocks is block B touching?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
Block B is touched by block A from below, block C from above, and block F from the right side. This makes for a total of 3 touching blocks.
Question 2: A structure is built with identical blocks in three layers. The bottom layer is a solid 3x3 square of blocks. The middle layer is a solid 2x2 square of blocks centered on the bottom layer. The top layer is a single block centered on the middle layer. How many total blocks are in the structure?
- 13
- 18
- 14 (Correct answer)
- 9
Correct answer: 14
The bottom layer has 3x3=9 blocks. The middle layer has 2x2=4 blocks. The top layer has 1 block. The total number of blocks is the sum of the layers: 9 + 4 + 1 = 14 blocks.
Question 3: A structure consists of three adjacent columns of blocks. The left column is 3 blocks high, the middle column is 2 blocks high, and the right column is 4 blocks high. The columns are flush against each other. How many other blocks is the bottom block of the left column touching?
- 1
- 2 (Correct answer)
- 4
- 3
Correct answer: 2
The bottom block of the left column touches the block directly above it in the same column and the bottom block of the middle column to its right. It does not touch the rightmost column. Therefore, it touches a total of 2 blocks.
Question 4: A structure is built on a 3x3 grid. The number of blocks in the column at each position is given: Row 1 (front): [2, 3, 1] Row 2 (middle): [1, 2, 2] Row 3 (back): [2, 1, 1] Consider the block at the very bottom of the center column (Row 2, Column 2), which has a height of 2. How many other blocks is this specific bottom block touching?
- 3
- 6
- 5 (Correct answer)
- 4
Correct answer: 5
The specified block is the bottom block in the stack of 2 at the grid's center. It touches: 1) the block above it in the same stack, 2) the bottom block of the stack in front of it (Row 1, Col 2), 3) the bottom block of the stack behind it (Row 3, Col 2), 4) the bottom block of the stack to its left (Row 2, Col 1), and 5) the bottom block of the stack to its right (Row 2, Col 3). This is a total of 5 blocks.
Question 5: A large 3x3x3 cube is created by gluing together 27 smaller, identical cubes. If the entire outside of the large cube is painted red, how many of the smaller cubes have no paint on them at all?
- 1 (Correct answer)
- 8
- 9
- 26
Correct answer: 1
In a 3x3x3 cube, only the single cube at the very center is not exposed to the outside. This central cube is surrounded on all six faces by other cubes. Therefore, only one cube will have no paint on it after the exterior is painted.
Question 6: A structure of identical blocks has a front view that is a 3-block wide, 2-block high solid rectangle. Its right-side view is a 2-block wide, 2-block high solid square. Assuming no blocks are floating, what is the minimum number of blocks needed to create such a structure?
- 12
- 6
- 9 (Correct answer)
- 8
Correct answer: 9
The front view requires a 2-block high column in each of the 3 width positions. The side view requires a 2-block high column in each of the 2 depth positions. This can be achieved with a minimum of 9 blocks by creating a configuration like a checkerboard of 2-high and 1-high stacks on the 3x2 base, for example: First row heights [2, 1, 2], Second row heights [1, 2, 1]. Total blocks = 2+1+2+1+2+1 = 9.
AFOQT - Air Force Officer Qualifying Block Counting Spatial Apperception Questions and Answers 1
Imagine a single stack of 4 blocks, labeled A, B, C, and D from bottom to top.
A second stack of 2 blocks, labeled E and F from bottom to top, is placed directly to the right of the first stack, with block E touching block A and block F touching block B.
How many blocks is block B touching?