ALIBI: honest witnesses and liars
Something happened. A handful of witnesses each give a statement, and every witness is one of two kinds. Honest witnesses say only true things. Liars say only false things. Your job is to mark each card honest or lying so that every statement comes out consistent with its speaker's kind. There is always exactly one way to do it, and you can reach it by reasoning alone. ALIBI is the knights-and-knaves puzzle of logic textbooks, dressed as a case file and generated fresh every day.
The move
Tap a witness card to cycle it through Unknown, Honest and Lying. When every card is marked, press Submit the case. A wrong submission tells you how many cards are wrong, not which ones, so guessing is expensive. The timer, hint count and wrong submissions make up your result for the day; the share text shows them as a grid and never reveals the answer.
Reading a statement
The rule to internalise: a statement is a claim about the world, and the speaker's kind tells you whether the claim is true or false. Nothing else. Some shapes that come up:
- "Morgan is lying." From an honest speaker, Morgan lies. From a liar, Morgan is honest. Either way the two are linked: they are of opposite kinds if the speaker is honest and of the same kind if the speaker lies.
- "Exactly three of us are honest." A count over the whole group including the speaker. If the speaker is honest the count is three; if not, the count is anything but three.
- "Avery and Blake are the same type." True means both honest or both liars. False means one of each.
- "Either Casey is honest or Drew is honest, but not both." An exclusive or. False means both are honest or neither is.
- "If Ada is honest, then I am lying." A conditional is false only when the first part is true and the second false. Follow it literally and it is much less scary than it looks.
- "The witness seated after me is lying." Some cases seat the witnesses in a circle; seat 1 follows the last seat.
One classic: nobody can say "I am lying". An honest witness would be lying and a liar would be telling the truth. A liar can cheerfully say "I am honest", though, so that claim tells you nothing on its own.
A worked case
Three witnesses. Avery says: "Blake is lying." Blake says: "Exactly one of us is honest." Casey says: "Avery and I are the same type."
- Suppose Blake is honest. Then exactly one witness is honest, and it is Blake, so Avery and Casey are liars. Avery's statement "Blake is lying" would then be false, which fits a liar. But Casey, a liar, says "Avery and I are the same type", which must be false; yet both are liars, so it is true. Contradiction. Blake is lying.
- Blake lying means the honest count is not one. Avery's claim "Blake is lying" is true, so Avery is honest.
- If Casey were lying, Casey's statement would be false, so Avery and Casey differ: Avery honest, Casey lying, consistent so far. But then exactly one witness (Avery) is honest, and Blake's statement would be true while Blake is a liar. Contradiction. So Casey is honest, which also makes Casey's statement true (both honest) and the honest count two, which keeps Blake's claim false.
Answer: Avery honest, Blake lying, Casey honest. Notice the method: assume, follow every statement that touches the assumption, and let a contradiction do the work. That is the whole technique; harder cases just have longer chains.
How to actually solve one
- Find a statement that pins someone down by itself. Counting claims and claims about the speaker's own group are the usual anchors.
- Pick a witness and assume honest. Trace the consequences through every statement that names them. A contradiction means they lie, and now you know something for certain.
- Mark what you know. Each statement card highlights the witnesses it talks about, so you can see what the remaining statements force next.
- Use the notebook for long chains. Writing "if A honest then B lies then C's count fails" beats holding it in your head.
Hints are never guesses
When you press Hint, the game runs its solver over every classification that is still consistent with what you have marked and tells you only what the evidence proves. The first press points you at the statements worth reading; a second press shows the full deduction and offers to mark the card for you. Hints count on your result, so they cost pride, not correctness.
Modes and scoring
- Daily case: one shared case per UTC day, recorded once. The difficulty tier follows the weekday, so some days are harder than others on purpose.
- Endless: generated cases at four tiers, as many as you like.
- Challenge: five cases in a row with three hints for the whole run. Score is 1000 per case plus a difficulty bonus, minus 100 per hint and 150 per wrong submission, minus a little for time beyond the first minute. Flawless runs earn an accuracy bonus and hint-free runs an efficiency bonus.
- Tutorial: a sixty-second case that teaches the move.
How a case is proved fair
Every case comes out of a seeded generator, so the daily is the same for everyone without a server deciding it. The generator writes statements from a fixed set of shapes, then an exhaustive solver tries every possible honest-or-lying assignment of the witnesses. A candidate case is kept only if exactly one assignment makes every statement consistent; cases with no answer or several are thrown away. In the last stress run over ten thousand seeds per tier, every case served had one solution. No language model is involved in generating or checking cases, which is why the hint can promise to tell you only what is provable.
Questions people ask
Can two witnesses contradict each other and both be right?
No. If two statements cannot both be true, at least one speaker is a liar. That is often the anchor you are looking for.
Does "us" include the speaker?
Yes. Counts are always over the whole group.
Is a statement ever half true?
Never. Each statement is one claim, fully true or fully false. Compound statements like "A is honest and B is lying" are false if either half fails.