Lesson: Jinx Puzzle
Student
Teacher
Extensions

The teacher should start out by saying: "Today, I'm going to jinx everyone. Take out your notebook or a piece of paper and do the following steps."


1. Choose a number from 1 to 10 and write it down.
2. Add 11.
3. Multiply by 6.
4. Subtract 3.
5. Divide by 3.
6. Add 5.
7. Divide by 2.
8. Subtract the number you started with in step 1.
9. Your answer is _____.

Teacher waits for a student and then asks a student who is done and looking up: "What did you get?" (13) If the student doesn't get 13 move on to another student and ask the same question. Continue until there is a consensus that you get 13.

Teacher says: Wow. All (or most) of you got 13! That must mean you all started with the same number. Is that right? (Heads should move side to side along with some "no" answers.)
Teacher: No? What did you start with then?
The teacher writes the numbers the students started with on the white board.

Teacher: Do you think it matters what number you started with? (Students will usually not be sure.)

Teacher: OK, let's try a few more numbers to see if this pattern continues.

The teacher then challenges them to come up with a number that will “break” the jinx. Students try larger numbers, fractions, negative numbers, etc. but come away frustrated declaring that “it must always work” mostly because the task becomes so tedious even with a calculator.

At this time the teacher introduces the Jinx calculator. Actually, it’s just a spreadsheet file in disguise that does the calculations for them so they can try more ambitious numbers.

After lots of trial and error with no success, the teacher tells the students to try 3000000000000000. (That’s 3 followed by 15 zeros.) Result as expected is still 13. Now click in B1 and add a 16th zero. Surprise! You should see 0. Now does that mean the trick no longer works? Or is it just that our Jinx calculator has some flaws? (It’s the latter.) Spreadsheets “fall apart” when we use numbers out of their range.

To prove that the trick really does work all the time, the teachers suggest the use of something that can represent any number chosen including ones you can’t completely write out like pi or the square root of 2. The teacher then uses the marbles and bags model (first introduced to me by W. W. Sawyer) and demonstrates why it works using a digital white board.
This is one of my favorite lessons which I usually do with a pre-algebra class.





















The “correct” answer of course is no, since we can prove it using algebra. But since this is a pre-algebra class the students are usually not sure.














An Excel version is available here.



Can that number Pi be used with the Jinx calculator? No, only an approximation like 3.14 is possible.

Let's try a different way to answer the question. Start with the puzzle again.

Step 1: Pick a number.
Instead of picking a specific number, let’s choose to use something that could
represent any number. Let’s use a bag.

The bag can contain any number you pick.

Step 2: Add 11



To show 11 we will use 11 small circles or “marbles”. Now we have a bag and 11 “marbles.”

Step 3: Multiply by 6


We have 6 bags and 66 marbles.

Step 4: Subtract 3


Now we have 6 bags and 63 marbles.

Step 5. Divide by 3


What's left? 2 bags and 21 marbles.

Step 6. Add 5


There are 2 bags and 26 marbles.

Step 7. Divide by 2



and we have 1 bag and 13 marbles.

Step 8: Subtract the number you picked in step 1.



But that’s the bag. You subtract the bag! So you are left with only 13 marbles or just plain 13.

Can you explain why this puzzle always gives you 13?

Students should walk away from this activity with an appreciation for the power of variables.




Source: Original Version 1.0 developed at CIESE- 
Center for Innovation in Engineering & Science Education (2007)
Revised 10.24.22 currently under construction