By the Numbers

(First published, July 2001)

Quick, look at these sets of three numbers:

3; 6; 7

14; 28; 29

5; 10; 11

2; 4; 5

Review these sets to discover the pattern among the three numbers in each set.

Now write (or say) a few more sets of three numbers that follow the same pattern.

This discovery activity is the basis for the following quick jolt.

(Spoiler alert: I am probably going to irritate you.)


To explores causes and consequences of stereotyping.


Any number, playing in a parallel fashion


5 - 10 minutes


Brief the players. Tell them that you are going to present a few sets of three numbers. Ask them to listen carefully and discover the pattern among the three numbers in each set. Present the four sample sets listed above.

Invite participation. Most players will have a knowing grin and some may blurt out their explanation of the relationship among the numbers. However, ask everyone to listen carefully to your instructions. Tell them to supply you with test sets by yelling out three numbers. Ask the players to wait until you have said “Yes” or “No” to each test set before offering the next one.

Provide feedback. Players will give you test sets that fit this pattern: n, 2n, 2n+1 (any number, twice that number, one more than twice the original number). Listen to each set and say “Yes” to confirm that it follows the pattern.

Nag the players. After verifying a few test sets, ask the players how they are feeling. Comment on the smug look on most faces. Present the following information, in your own words:

Many of you are falling into the trap of hasty generalization. You found a formula that links the numbers. You immediately start proving your hypothesis by offering a test set that fits the formula. You feel happy when your test set gets a “Yes”. You offer more test sets of the same type and enjoy feeling smart and superior. You don't present a test set that doesn't fit the formula because if you get a “No” everyone will think that you are stupid. You yourself will feel stupid.

A true scientist, however, keeps an open mind. She attempts to disprove her hypothesis. So how about if you try some test sets designed to get a “No” from me.

Give feedback. Here's where the jolt comes: In spite of how it might appear, the pattern is simply any three whole numbers in ascending order. According to this formula, these test sets will receive “Yes”:

7; 9; 10

19; 24; 25

10; 20; 2,000

8; 60,000; 7,000,000,000

And these test sets will receive “No”:

5; 9; 9

12; 200; 9

98; 15; 3

Listen to new test sets and answer “Yes” or “No” according to whether they contain three whole numbers in ascending order.

Return to your nagging. Whenever someone's test set receives a “No”, ask the person how she feels. Explain that most people feel depressed when their hypothesis is rejected. Actually, a “No” provides valuable information, sometimes more valuable than a “Yes”.

Speed up the process. Explain that you are going to try out some more test sets yourself. Use crazy sets of numbers (such as “5; 78; 2,365,897”) and give a resounding “Yes” to each.

Explain the pattern. Ask players to tell you the formula or the pattern that you are using. Confirm the formula of any three whole numbers in ascending sequence.

Relate the experience to the process of stereotyping. Explain that this simple activity illustrates the human tendency to stereotype things, including people from other cultures.

Just because we meet a small sample of people from a different culture who share a few common characteristics, we assume that everyone in that culture will share the same characteristics. We strengthen this narrow opinion by selectively looking for the same characteristic among new members of the culture. We don't pay attention to other unique characteristics that would challenge our hypothesis. We may actually feel upset if someone does not conform to our stereotypical perception.

Encourage players to share real-world experiences. Ask for examples of being surprised by the unexpected behaviors of people from other cultures. Conclude the session by encouraging participants to try to disprove their own assumptions and hypotheses.