A cuckoo lays her egg in somebody else's nest, and the bird who built it cannot tell. That is the whole puzzle. One egg in today's clutch is not yours, you cannot see which, and nothing you are allowed to do will ever tell you about a single egg. The balance compares two groups. The lantern says whether the stranger is anywhere among a group. On the crowded days you can cup a few in your hands and count how many hearts beat out of time. Everything you learn arrives about a crowd, and the work is turning crowds into one bird.
Why it exists
The shelf already had a daily that asks you to guess well. HUNCH gives you one strange question a day and measures your gut. What it never had was a daily with a right answer, and that turns out to be the thing people come back for: the same puzzle for everybody, one attempt, a result you can hand to a friend without spoiling it. So CUCKOO is muplu's first daily you can be certain about, and the certainty is enforced rather than encouraged.
The nest will not take a guess
You can only name an egg when the tests you have run leave exactly one possible nest. Point at the right egg too early and the nest simply does not take it, at no cost, because a lucky poke is not an answer. It also means nobody can brute-force a day, and every solve on the board is a real deduction.
The pencil is yours, the answer is not
Tapping an egg with the pencil on crosses it out or rings it. Those marks are your own notebook and the toy never fills them in for you. All it will tell you is how many nests still fit everything you know, which is a measure of progress, never a hint about which.
Par is not a designer's guess
Every day carries a par, and nobody picked it. It is the information bound: with a balance, one test has three possible outcomes, so t tests can tell apart at most three to the power of t different nests, and par is the smallest t where that is enough. Twelve eggs need three. Sixteen eggs with two cuckoos hiding among them need five. On the day the balance is broken the tests only answer yes or no, so the base drops to two and par climbs. It is a floor, so a lucky clutch really can be found in fewer, and the toy says so rather than pretending otherwise.
This is group testing, and it was a real problem
In 1943 Robert Dorfman was looking at how to screen huge numbers of army recruits for a disease when only a few would have it. Testing everyone one at a time was hopeless. Pooling the samples and testing the pool was not: one negative result cleared the whole group at once. That idea is now called group testing, it is why pooled screening works, and it is exactly what the lantern does. The balance is the older cousin, the counterfeit coin puzzle, where three outcomes per weighing beat two and the arithmetic runs in base three instead of base two.
The week is a shape
Monday is five eggs and a kind afternoon. By Wednesday the nest is full. On Thursday nobody has said whether the cuckoo's egg is heavier or lighter, which quietly ruins the obvious weighings. On Friday the balance is broken and the lantern is all you have, so par climbs. Saturday and Sunday hide two of them and lend you the listen. Sunday is meant to be hard.
Nothing is taken away from you
Every day you solve hatches into a bird that lives in your tree and never leaves it. Miss a day and one of two banked forgivenesses covers it instead of the streak going to zero. There is no guilt copy anywhere in this toy, on purpose.
The quiet parts
No account, no ads, nothing following you around. The puzzle is computed in your own browser from the date, which is why everybody in the world opens the same nest and why the whole thing still plays with the network down. The only thing that ever leaves the page is one number, how many tests you needed, so the chart at the end can show you what everybody else needed. It cannot reveal an answer, because it never knew one.