Half-Life Detective
The server picks a starting number of nuclei and a check time, and a target for how many should still be undecayed then (always achievable). You choose the half-life, and a real radioactive-decay model counts what is left. Hitting the target refunds your run.
About this simulation
What it shows
A puzzle on a sample of radioactive nuclei. You are given the starting number of nuclei and a check time, plus a target for how many should still be undecayed then. You choose the half-life, then run it.
The key idea
In every half-life, half of the nuclei still left decay, so the count falls by the same fraction in each equal stretch of time. After a time T, the share left is (1/2) raised to T divided by the half-life.
Try this
Run it once, see whether too many or too few nuclei are left at the check time, then choose a longer half-life to leave more or a shorter one to leave fewer.