I run a lunchtime chess and logic club at my School for 10-12 year olds. The chess players need no inspiration, but I require new ideas for the logicians.
So far I’ve used lateral thinking puzzles (I give them a situation ‘A man enters a field and dies’, then answer their questions with only ‘yes’, ‘no’ or ‘irrelevant’),
card tricks and logic puzzles (Martin Gardner is particularly useful here).
My favourite is a logical deduction game using cards:
For three players, take 2 red cards and 3 black cards.
Shuffle well.
Give each player a card face down, which they place on their forehead, so the other two can see the colour (but they can’t).
Now the logic begins.
Can any player immediately deduce the colour of his card?
(If one player can see two red cards, he can state he must have a black card.)
If not, given that no player can state anything immediately, can any player now say what they have?
(If two players can see one red card, they can each state they must have a black card, because otherwise someone would have spoken up.)
And so on.
You can also get spectators to make deductions, based on which players make a claim.
If you’ve read this far, thank you.
What I’d like is ideas to get my pupils thinking. They should be solvable in 5-10 minutes, preferably involve a group (say from 5-15) and be fair and logical.
If you can come up with another logical game, that would be splendid!
Raymond Smullyan is a good place to go. A lot of truth-teller/liar type problems. They tend to build from simpler to more complex, so the easier ones go pretty quick, the harder ones might take longer.
Another good for a group - do the ‘prisoners and hats’ problem[sup]*[/sup]. This would work well since you could have them actually act out the problem - trying out each solution and figuring out ways to improve it.
You could kill two birds with one stone with chess retrograde analysis problems. If you’re unfamiliar with them, they involve looking at a chess board and figuring out what happened prior to the current move. Smullyan’s The Chess Mysteries of Sherlock Holmes covers a fair number, or look online for other puzzles.
[sup]*[/sup] The day before their execution, a group of prisoners is told what will happen : They’ll be seated in a row so that each person can only see those in front of them. Black and white hats will be picked at random and placed on each person’s head. Then they will be asked, one at a time (they get to pick the order), what color hat they are wearing. Those that answer correctly will be spared. Each prisoner will be able to hear the response and fate of the others. What strategy do they come up with the night before to maximize their chances of survival?
William Wu has one of the best collections of puzzles like this. I’ve linked to the Easy section, but you might want to look in Medium too. The Hard section is probably too hard for most 12-year-olds.
Note that Mr. Wu doesn’t provide answers, preferring that people work them out for themselves, and you should be able to solve most of the Easy section. If you are stuck, you’ll find the answers in the user forum
A lot of simple results from number theory require little more than lateral thinking. Cantor’s diagonalisation proof is also amazingly simple, yet requires lateral thinking.
Of course, their relevance is dependent on just how bright these kids are and to what maths they have been exposed to.
Have you considered starting them on Sudoku puzzles? Sudoku is a number game where you have to logically deduce where the missing numbers go in the puzzle. Most newspapers are publishing them nowadays. More info on sudoku can be found here (with a basic strategy guide). More basic strategies can be found here while advanced strategies can be found here.
Yes it is, as is his Aha! Gotcha! Since the OP mentioned Martin Gardner, it’s possible he’s already familiar with these, but they are worth mentioning.
