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Chapter 2. The NOT-AND machine

You need Chapter 1.

A new machine

Remember: you want the machine to show YES, the trickster wants NO, and he puts his note in after you. (We write the notes in small letters — "yes", "no" — and the light in capitals — YES, NO.)

In the last chapter we learned the secret of the OR machine: put in a "yes" and the trickster is powerless. Maybe "yes" always helps?

No. Here is another machine — and on it everything is the other way round.

It is called NOT-AND. It shows NO only when both notes say "yes". In every other case it shows YES.

The table, as always, is known in advance:

first note   second note   light
yes          yes           NO
yes          no            YES
no           yes           YES
no           no            YES

NO appears in only one case — when both boxes hold "yes".

Let's try

First time. You put in "yes", as in the last chapter. The trickster looks — and puts in a "yes" too. Yes and yes — NO. The trickster got what he wanted.

So the familiar secret doesn't work here.

Second time. You put in "no". The trickster thinks. If he puts in "yes", the table says YES. If he puts in "no" — YES again. Whatever he does, the machine shows YES. The trickster is powerless.

The secret of the NOT-AND machine:

Put in a "no" — and the trickster can do nothing.

And again it doesn't matter whether your box is the left or the right one.

Why

To get NO, both notes must say "yes". Yours says "no" — so that can't happen, whatever the trickster puts in.

Compare the two machines:

OR        for NO it needs two "no"s    →  put in "yes"
NOT-AND   for NO it needs two yeses    →  put in "no"

With your note you wreck the trickster's plan.

And if both boxes are the trickster's?

He puts "yes" in both — and the machine shows NO. Just as with OR: against two of his boxes you can do nothing.

An example from life

The NOT-AND machine lives wherever there is a rule "not both at once".

Say a movie theater has this rule for a 12+ movie: you are turned away only when both conditions hold at once — the viewer is under 12, and has no adult with them. In every other case you get in. That is exactly the NOT-AND machine: the answer to "let in?" is NO only when both notes say "yes".

"the viewer is under 12"    yes   yes   no    no
"has no adult with them"    yes   no    yes   no
let in?                     NO    YES   YES   YES

You are 13 — that you know for sure, that is your box: "under 12" — "no". But "with an adult or without" depends on whether the cashier sees one; maybe the cashier won't even notice your mom in line. You don't fill that box.

But it doesn't matter to you what ends up there. Your box holds "no" — the two notes can't both say "yes". You get in.

Your little brother is 10. His box holds "yes". Then everything depends on the second box: if he comes with mom, he gets in; if they decide he's alone, he doesn't.

Try it with a friend

On slips of paper, as in Chapter 1. One of you is the trickster. Try putting in "yes", then "no". See for yourself: with "no" the trickster can do nothing, with "yes" he can.

Puzzles

  1. The NOT-AND machine. What should you put in your box so that the trickster is powerless?
  2. You put in "yes". What does the trickster put in, and what does the machine show?
  3. On which machine does "yes" help, and on which does "no"?

Think it through first, then check.

Answers. 1 — "no": then the two notes can't both say "yes". 2 — he puts in "yes", and the machine shows NO. 3 — "yes" helps on the OR machine, "no" on the NOT-AND machine.

In the next chapter: the "if… then" machine. Its two boxes are different, and that changes everything.