Blueprint & Beyond — Mental Challenge
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Game 1 — The Hidden Squares
How many squares can you find in the diagram? Count squares of all sizes.
Count triangles of all sizes, including overlapping triangles.
5 machines + 5 minutes = 5 products
How many minutes for 100 machines to make 100 products?
Hint: Try changing your viewing perspective.
Solution: 14 Squares
Look at Every Size
The lesson: do not count only the obvious individual cells. Look for overlapping combinations and the whole picture.
🔓 Solution — 0 4 2
Keep the five clues above in view as you follow each step.
Step 1 — Cross out 7, 3, 8. The orange clue (738) says none appears in the code.
Step 2 — Find 0. The purple clue (780) means 0 is in the code, but NOT last.
Step 3 — Place 2 last. In the red clue (682), 8 is excluded. The red clue says exactly one digit is correct and correctly placed. The green clue says two digits from 206 are correct but misplaced. Therefore 2 is last and 6 is not in the code.
Step 4 — Place 0 first. The green clue (206) says both 2 and 0 are in the code but in different positions. Since 0 cannot be middle or last, it goes first.
Step 5 — Fill the middle with 4. The blue clue (614) gives 4 as the one correct digit, but not in its displayed position (third). The middle slot is free.
Final code: 0 — 4 — 2. Check all five clues to confirm.
Learning takeaway: Combine evidence, eliminate assumptions and verify constraints before deciding.
Solution: $0.05 (5 cents)
Look at the original question above while checking the calculation.
Ball: $0.05
Bat: $1.05
Total: $1.10
Difference: $1.00
Learning takeaway: Challenge your first instinct. Good decisions require critical thinking, not just quick answers.
Solution — 18 Triangles
Look at the original triangle above. There are four sloping lines meeting at the top, and three horizontal levels where triangles can end.
At each horizontal level, choose any two of the four sloping lines to form a triangle: 6 triangles per level × 3 levels = 18 triangles.
Learning takeaway: Use a systematic approach to avoid overlooking possibilities.
Solution — 5 Minutes
Each machine produces one product in five minutes. If 100 machines work at the same time, each produces one product, so 100 products are finished in 5 minutes.
Learning takeaway: Parallel work changes total duration.
Solution — Space 87
Imagine rotating the parking lot 180 degrees. The numbers then read in sequence: 86, 87, 88, 89, 90, 91. The car is parked on 87.
Learning takeaway: Changing perspective can reveal a simple answer.