The Jinx Puzzle

Part 1: Here is a puzzle that will always “jinx” it. Try it with 3 different numbers to make sure it works.

Pick a number between 0 and 1
Add 11
Multiply by 6
Subtract 3
Divide by 3
Add 5
Divide by 2
Subtract original number
Your Answer is:

Part 2: Do you think this puzzle will always work for any number you choose?

To find out try it with ANY number using your calculator. An example is done for you below.

Press / On your Home screen you should see this:
Pick any number / 75 / 75
75
Add 11 to previous answer / + 11 / Ans + 11
86
Multiply previous answer by 6 / * 6 / Ans * 6
516
Subtract 3 from previous answer / - 3 / Ans - 3
513
Divide previous answer by 3 / / 3 / Ans / 3
171
Add 5 to previous answer / + 5 / Ans + 5
176
Divide previous answer by 2 / / 2 / Ans / 2
88
Subtract the original number from previous answer / - 75 / Ans - X
13

Try it for at least 2 more numbers. Include a mixed number and a negative number.

Note: To create a negative number start by pressing the _ key.

Questions:

1. Do you think you will always get 13 no matter what number you try? Why or Why not?

2. How would you prove that the Jinx puzzle always works for any number?

3. Write an equation that demonstrates why the steps above always equals 13.

Part 3: Teacher’s Notes and Solutions Extensions

Question 1. Based on all numbers tried in class you should always get 13. From this conclusion you should have a strong suspicion that it will always work. But we can’t be sure unless we can try in some way to test all numbers. In other words, we would need to prove it.

Question 2. So, how would you prove that the Jinx puzzle always works for any number?Instead of picking a specific number, let’s choose to use something that could represent any number. Let’s use a bag. In Algebra we can use B to represent the number inside the bag.

In Pictures / Using Algebra
Step 1. Choose a number / / B
Step 2. Add 11
To show 11 we will use 11 small circles or “marbles”. Now we have a bag and 11 “marbles”. / / B + 11
Step 3. Multiply by 6
We have 6 bags and 66 marbles. / / 6B + 66
Step 4. Subtract 3
Remove 3 marbles from the previous picture. We now have have 6 bags and 63 marbles / / 6B + 63
Step 5. Divide by 3
This results in 2 bags and 21 marbles. / / / 2B + 21
Step 6. Add 5
Adding 5 marbles you have 2 bags and 26 marbles. / / / 2B + 26
Step 7. Divide by 2 / / B + 13
Step 8: Subtract the number you chose in step 1. That’s the bag which you subtract. So you are left with 13 marbles or just plain 13. / / 13

Question 3. (((X+11) * 6 – 3) / 3 + 5) / 2 – X = 13