1. Math Maze Worksheet
The challenge:
Start in the top left corner, add the decimals and use your answers as a guide to the end of the maze. Avoid jail cells and win this maze game by successfully solving all questions.
Download the printable maze (PDF)
2. The Magic Square Puzzle
The challenge:
Create a 3×3 magic square using numbers 1 to 9 where each row, column, and diagonal sums up to 15.
The solution:
A common solution is:
2 | 7 | 6
---+---+---
9 | 5 | 1
---+---+---
4 | 3 | 8
Each row, column, and diagonal adds up to 15.
Try it: 2 + 7 + 6 = 15. 9 + 5 + 1 = 15. 4 + 3 + 8 = 15. Both columns and both diagonals work out the same way.
3. The Monty Hall Problem
The challenge:
Decide whether to stick with your initial door choice or switch after a goat is revealed.
The solution:
It's better to switch doors. Initially, the probability of selecting the car is 1/3. If you switch after a goat is revealed, the probability of winning the car is 2/3. This counterintuitive result arises because the host's action of revealing a goat changes the probabilities — the door you didn't pick now carries the combined odds of the two doors you didn't choose initially.
4. The Bridge Crossing Conundrum
The challenge:
Determine if four people with crossing times of 1, 2, 5, and 10 minutes can all cross in 17 minutes or less using one flashlight.
The solution:
- First, the 1-minute and 2-minute cross with the flashlight (2 minutes).
- The 1-minute returns with the flashlight (1 minute).
- The 5-minute and 10-minute cross with the flashlight (10 minutes).
- The 2-minute returns with the flashlight (2 minutes).
- Finally, the 1-minute and 2-minute cross again (2 minutes).
Total time = 2 + 1 + 10 + 2 + 2 = 17 minutes.
5. The Handshake Problem
The challenge:
Determine the number of handshakes if there are 10 guests.
The solution:
Use the formula for the handshake problem: n × (n − 1) / 2, where n is the number of guests.
For 10 guests:
10 × 9 / 2 = 45 handshakes
This formula arises because each of the n guests shakes hands with the n − 1 others, then we divide by 2 to avoid double-counting (your handshake with me is the same handshake as my handshake with you).
6. The Infinite Chocolate Paradox
The challenge:
Explain the "creation" of an extra piece from splitting the chocolate.
The solution:
This paradox usually occurs due to a re-arrangement trick that creates an illusion of an extra piece. It involves making cuts that slightly shift the geometry of the pieces such that gaps are created and refilled without increasing the total chocolate. It's an example of a geometric puzzle that plays on perception.
These solutions not only solve the challenges but illustrate the logical and analytical skills developed through such exercises. Enjoy the process of problem-solving!