Daily Triplets

Daily Triplets is Wason's 2-4-6 task turned into a daily, and it names that source itself. A secret mathematical rule decides which triplets of digits are accepted. You feed it triplets, it answers with a tick or a cross, and when you think you have worked out what it is thinking you write the rule down as a mathematical condition. Testing is unlimited. Stating the rule is not: you get three goes at it. The board opens with a single triplet already known to fit, and everything after that is yours to choose.

1. Press PLAY. The board opens on one triplet that the game confirms fits the day's rule, as a place to push off from.
2. Type any three digits from 0 to 9 into the slots and press TEST. The answer comes back as a tick if the triplet satisfies the hidden rule and a cross if it does not.
3. Keep testing. The help panel says outright that there is no limit on how many triplets you try.
4. Press I KNOW THE RULE and write the rule as a mathematical condition. You have three attempts at it.

Almost every daily puzzle sets a fixed problem and asks for the answer. This one hands you an oracle and asks you to work out what it is thinking, which is a different sport altogether, closer to running an experiment than to filling in a grid. The 2-4-6 task is famous because nearly everybody fails it in the same way, by only asking questions they expect a yes to, and playing it every day is an unusually direct way of catching yourself in the act. Free tests against a hard limit of three statements is precisely the right shape for that lesson.

Binary, and that is the whole design. Every test comes back as a tick or a cross and nothing else, so all the information in the game comes from which triplets you decided to try. The clever part is at the end: the help panel says your equation is checked against all triplets rather than against a particular form of words, so you can express the rule however you like and still be marked right if it accepts and rejects the same things.

Daily

One hidden rule per day, numbered, with the board opening on a single triplet that is known to fit.

• Try to break your own theory instead of confirming it. This is the exact trap the Wason task was built to expose: people test triplets that fit the rule they already suspect, collect ticks, and mistake them for proof. A cross is worth more, because a theory that survives an attempt to kill it is one you can safely write down.
• Tests are free and statements are not, so over-test. Three wrong statements end your day, while a hundred extra tests cost nothing at all.
• Vary one digit at a time. A triplet that differs from a known-good one in a single position tells you which position the rule cares about; changing all three tells you almost nothing.
• The board asks for a mathematical condition, so the rule is a relationship between the three digits rather than a fact about any one of them. Order, differences, sums, parity and repeats are the raw material.