Where this idea comes from
The counterfeit coin
During and after the Second World War a puzzle spread among mathematicians: twelve coins, one fake that is a little lighter or heavier, and a balance you may use three times. In 1946 the physicist Freeman Dyson wrote a paper about it, “The problem of the pennies”.
One thing to hold: A two-pan balance and a pile of coins that look the same.
Why it matters: Each weighing has three possible results — left heavier, right heavier, or level — so three weighings can tell apart up to 27 cases. Planning around those three results is the whole puzzle. The version here is gentler: the fake is known to be heavier, so two weighings are enough for nine coins.