Prof. Andrew Stapleton at the U. of Wisconsin-Lacrosse shares a teaching tip when discussing random numbers.
Predict a “random number” by alternating four-digit contributions. Start by determining a 5- digit number and writing it down in dark ink on a large piece of paper and sticking it in your briefcase. I act like I am picking random numbers, but I know exactly how to get to the number I have pre-determined.
Here is an example: I tell my class, “Let’s pick some numbers, I’ll start”: 4729 Mine I already know that the final number – the one written on the large piece of paper in my briefcase is 24727.
I then ask for two students to give me each a two-digit random number. The greater the number of participants the greater the impact. Student one chooses “58” and Student 2 chooses “32.” So 5832 yours
4167 Mine I act like I am thinking about another random four-digit number, but what I am doing is making their digits and mine add to 9999. (i.e., 5832 + 4167 = 9999)
I again ask two different students to each give me a two-digit random number. One gives me “69” and the other “02”. So 6902 yours
3097 Mine Again I make theirs and mine add to 9999, but I don’t do it right away. In fact, I act like I am really just pulling my digits out of thin air.
Sum = 24727. I then add all of these together. I tell them I had a dream about what number we would collectively come to in this exercise and wrote it down on a piece of paper and I get it out and unfold it. Once they see it matches, they are baffled and are eager to learn how I did it.
Solution: I simply take my original 5-digit number and subtract 2 from the last digit and put it in front of the first. This is because whatever you choose – I will choose digits that add to 9. So, the second set adds to 9999 and the third set adds to 9999 – just shy of 20000, in fact 19998. So, I subtract those two from the end and stick the “2” in the front.