5 Discrete Mathematics

5.1 More pointed at than pointing

Gather yourself and a few friends

into a circle and point at each

other in some arrangement of

pointing. Let each person point

at one or more of the others, or

at themselves, or at nobody, as

they like. Use both hands, or

different fingers, or your feet if

you want to point at several peo-

ple, and let us say that it is al-

lowed to point more than once at

a given person, or at several peo-

ple, or at yourself—go to town!

Perhaps some people are pointing

quite a lot and others are point-

ing much less, and similarly with

being pointed at. Now, I have a

question about whether you might be able to achieve a certain feature in your pattern of

pointing at each other.

Question 33. Can you arrange it so that every person is altogether more often pointed at

than pointing?

In other words, could we all be pointed at strictly more times than we point at others?

Ponder the problem on your own, before reading further.

Interlude. . .