You’re always pushing limits, so I’ve got a puzzle that’ll test your discipline and might just give you a mental edge for the next sprint.

First weigh three balls against another three. If the scale tips, the heavy ball is on that side. Take two of those heavy‑side balls and weigh them against two of the light‑side balls. If the scale tips again, the heavier side contains the odd ball – you’ve found it. If the scale balances, the odd ball is the one you didn’t put on the scale from the heavier side. If the first weighing balances, the odd ball is one of the two left over; just weigh those two and the heavier one is the odd one out.

First weigh 4 balls against 4. • If they balance, the odd ball is in the 4 you didn’t weigh. - Weigh 3 of those 4 against 3 known good balls. – If they balance, the remaining ball is odd, and you need the last weighing to see if it’s heavier or lighter by comparing it to a good one. – If they tip, the heavier side tells you whether the odd ball is heavier or lighter; the third weighing pinpoints which of the 3 it is by weighing two of them. • If the first weighing tips, you know the odd ball is in the heavier or lighter side and also whether it’s heavier or lighter. - Take 3 balls from the heavy side and 3 from the light side and weigh them against 3 from the heavy side and 3 good balls. – The outcome will narrow the possibilities to two or three balls with known heavier/lighter status. – Use the third weighing to compare the two remaining candidates (or a single candidate against a good ball) to decide which one is odd and its weight. That’s the three‑step trick—no extra math, just systematic elimination.

First weigh 4 balls against 4. If they balance, the odd ball is among the 4 you didn’t weigh. Then weigh 3 of those 4 against 3 known good balls. If that balances, the remaining ball is odd; weigh it against a good one to see if it’s heavier or lighter. If the 3‑vs‑3 tips, you’ll know whether the odd ball is heavier or lighter and which of the 3 it is with the third weighing. If the first 4‑vs‑4 tips, you know the odd ball is in the heavy or light side and whether it’s heavier or lighter. Take 3 from the heavy side and 3 from the light side and weigh them against each other or against good balls. The result will leave you with only two or three possible balls with a known heavier or lighter status. Use the third weighing to compare two of those candidates (or one against a good ball) and you’ll pinpoint the odd ball and its weight.

First weigh 8 against 8. If they balance, the odd ball is in the 4 you left out. Weigh 3 of those 4 against 3 known good balls. If that balances, the remaining ball is odd – weigh it against a good one to see if it’s heavier. If it tips, you know whether the odd ball is heavier or lighter and you’ve narrowed it to 3; the third weighing tells you which one. If the first weighing tips, you know the odd ball is on the heavier side and that it’s heavier. Take 3 balls from that side and 3 from the lighter side and weigh them against each other. The outcome will leave you with either 2 or 3 candidates with a known heavier status. Use the third weighing to compare two of those candidates (or one against a good ball) to pinpoint the odd one. That’s the 20‑ball trick in three moves – no wasted balance, just a laser‑focused elimination.