Paperclip Trick

For this puzzle, you’ll use three cups and eleven objects. The first challenge is to put an odd number of objects in each cup. Is this pretty simple? How many different combinations can you come up with for the eleven objects?

Download Student Worksheet & Exercises

Now how about if we take an object away and use ten instead? Is this puzzle more challenging? Here’s a hint: can you figure out a way for an object to be in two different cups at the same time? Work on this for a little while prior to watching the solution.

Pretty cool, right? I hope you enjoyed this trick. Mathematics and paradoxes can really be a lot of fun!

Exercises

1. What is an even number?
2. What is an odd number?

If you have 8 paperclips and three cups, arrange the paperclips you that you have an odd number in each cup. Find three different solutions (arrangements) to solve this problem.

3. First arrangement
4. Second arrangement
5. Third arrangement

Now you have 11 paperclips and three cups. Find two new solutions (ones we haven’t covered yet in this lesson) to having an odd number in each cup.

6. First arrangement
7. Second arrangement

Reduce your number to 10 paperclips. Find four new solutions (ones we haven’t covered yet in this lesson) to having an odd number in each cup. (Is it easier this time?)

8. First arrangement
9. Second arrangement
10. Third arrangement
11. Fourth arrangement