Challenge 07

Challenge #07

String Theory

Perform the probability experiment that is described below, and which is demonstrated in the video.

Have a partner hold six pieces of string (all of equal length) in their fist such that six ends of string stick out of the top of their fist and six ends stick out of the bottom. You should not be able to tell by looking which of the top-ends connects to which of the bottom-ends.
Choose two of the loose top-ends and tie them together with a knot. Then choose two of the remaining loose top-ends and tie them together. Then tie the last two top-ends together. Repeat this process with the bottom-ends.

What are the chances that the six pieces of string have been tied end-to-end and now form one continuous loop?

Explore this problem in any way that makes sense to you! Both experimental and theoretical approaches are possible.

Follow-up Challenges

What if we had used 4 strings? What about 8 strings?

What if we have used 2N strings? (Also: why is it better for us to say 2N strings here, as opposed to N strings?)

Consider the experimental data below, collected by real students around the world! What do you notice? What do you wonder?

	No. Trials	One Loop	Two Loops	Three Loops
01. St. John's Int'l School, Belgium	59	21	30	8
02. SAM Academy, Peru	6	3	3	0
03. Marissa Rodriguez, Texas, USA	10	6	3	1
04. Majorstuen skole, Norway	22	8	11	3
05. --	--	--	--	--
Totals:	97	38	47	12

Response Videos

Did you try this experiment? Reach out to share your data and we'll include it here! :)

Marissa's response video

Carin's response video