Spatial Reasoning Games: Summer Math Logic Camp Part 2

July 24, 2026

Summer Logic Camp (Part 2)

Welcome back to week two of our Summer Logic Camp Double Feature! If your family tackled our math riddles last week, your brain muscles are already warmed up. While Part 1 focused on algebraic values and clean grid balance, Part 2 is zooming into two completely different areas of elite analytical skill: Spatial Geometry and Optimal Path Optimization. These puzzles challenge students to think steps ahead, visualize changes in shapes, and map out strategic paths to maximize their final scores. Let’s dive straight into our final two camp challenges for July!

Puzzle #3: Toothpick Geometry (Spatial Reasoning)

The Mission: Look at the visual arrangement below. As it stands, it uses exactly 16 toothpicks to create a layout of 5 identical squares.

A set of 16 toothpicks arranged to create five identical squares. The challenge is to MOVE 3 to change it to 4 identical squares.

The Challenge: Move exactly 3 toothpicks to alter the shape so that it forms exactly 4 identical squares with no leftover or open-ended toothpicks.
The Rules: You cannot break the toothpicks, overlap them, or leave any loose, open-ended toothpicks hanging off the edges. Every single toothpick must actively form a border of one of the 4 identical squares!

Puzzle #4: The Path of Products (Arithmetic Mastery) The Mission: Start at the top-left corner box and track a pathway down to the bottom-right corner box.

A 5x5 grid with arrow pointing to the right or down from each number. The top row has 2, 5, and 1. The middle row has 4, 3, and 6. The bottom row has 1, 2, and 8. The challenge is to find the path that will create the greatest product.

The Rules: You can only move down or right along the grid tiles. As you pass through a number box, multiply it by your running total.
The Goal: Discover the exact pathway configuration that yields the largest possible final product!

Summer Logic Camp Master Answer Key

📁 [Click to Expand July 24th Solutions]

Puzzle #3 Solution:

To drop from 5 squares down to 4 identical squares using the same 16 toothpicks, you must create four squares each using four unshared toothpicks. By removing two toothpicks from the bottom left corner of the extended layout and one from the bottom right corner, you can create the fourth square using the unmoved toothpick on the bottom right. The toothpicks to be moved are changed to red.

Solution for Puzzle #3: A set of 16 toothpicks arranged to create five identical squares. The challenge is to MOVE 3 to change it to 4 identical squares.

Puzzle #4 Solution:

Let’s calculate the competing paths moving only down and right:

Path Alpha (Straight Top then Down):
Path Beta (Straight Left Down then Right):
The Winner (The Optimal Zig-Zag): Move from .

The path that unlocks the maximum product vault is 2 ➔ 5 ➔ 3 ➔ 6 ➔ 8, yielding a massive total of 1,440!

The MyTutorLesson Summer Strategy

At MyTutorLesson, we believe that true academic acceleration happens when a student learns to love the process of problem-solving. Puzzles like these lay the essential foundation for spatial geometry, logical algorithmic tracking, and algebraic substitution that students encounter in high school and college courses.

Whether your student needs to master fundamental K-12 math operations, sharpen their touch-typing speed, or gain an elite command of Microsoft programs, our private tutoring sessions are tailored to eliminate school stress and build long-term confidence.

Ignite your child’s analytical potential.

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Spatial Reasoning Games: Summer Math Logic Camp Part 2