## Wednesday, March 11, 2015

### Another number guessing game (actually 2!)

who: J2
when: evening/bedtime
where: bedroom
what material we used: a 100 board with removable tiles

We tried out two new number guessing games that J2 really enjoyed. In fact, he misunderstood the rules of the first game and ended up inventing the second one himself.

# Multiples

One player is the number master and the other players are guessers. The number master chooses a secret number and then says a clue, a multiple of the chosen number. We marked the clues on the 100 board for reference. After each clue, the other players make a guess about the secret number.

For tonight, I stayed with single digit secret numbers and, generally, just gave clues that were smaller than 50.

Some tips
When the correct answer was guessed, I asked J2 whether that was the only possible secret number compatible with the clues we had so far. That also led us to talk about what information each clue gave and to realize, without deeply exploring, that some clues are very restrictive (give a lot of information) while others don't help at all. It will be interesting for him to explore further to see what the differences are . . .

Other than through relative choice of clues, you can vary the difficulty by giving smaller or larger clues. Also, 2, 5, 3, 9 are relatively easy to recognize as factors, while larger primes are generally harder to spot. Of course, your mileage will vary with the experience of the particular players.

Marking the clues on the number board gives you the chance to see some nice multiples patterns, though this depends on how many clues are required before they guess the secret. If it seems fun, you can fill in the rest of the multiples pattern after the correct guess has been made.

# Factors

As a reverse version of the game, give clues that are factors of the chosen number instead of multiples. This was J2's invention and he had a sneaky plan in mind. The first number he chose was prime and then he refused to give any more clues!

# Some further explorations

If you play this game, you might enjoy thinking about some related questions:

1. Playing the multiples game, I gave a clue and J2 immediately guessed my secret number. What do you guess about my secret number that time?
2. Is any collection of clues possibly valid for the multiples game? The factors game?
3. Can the number master cheat at the multiples game? That is, if they don't write down their answer, can they change mid-game? Restricted to a 100 board, what sequence of clues will keep their options open the longest?
4. In the factors game, can the number master cheat? Is it easier or harder than for the multiples game? What if the secret can be as large as you want?