Countdown numbers game tips
The numbers round looks like arithmetic and plays like search. Here is how often a board is solvable, how many steps the best route usually takes, and three example boards worked step by step.
The rules in one paragraph
You get six numbers, usually a mix of "large" ones (25, 50, 75, 100) and small ones (1 to 10), and a three-digit target. You may add, subtract, multiply or divide two numbers at a time. Each number is used at most once, every result can be used again, subtraction must stay above zero, and division must be exact. You do not have to use every number. Parsum plays this daily and scores you on the number of steps against par, the fewest steps that can reach the target.
How often is a target reachable?
We sampled 1500 random boards-and-targets (targets from 101 to 999, small numbers drawn from two copies of 1 to 10, as in the show) with the same exhaustive search the solver uses. 92.9% had an exact answer. The mix of large numbers matters:
| Large numbers on the board | Targets reachable exactly |
|---|---|
| 0 large, 6 small | 88% |
| 1 large, 5 small | 96% |
| 2 large, 4 small | 98.3% |
| 3 large, 3 small | 94% |
| 4 large, 2 small | 88% |
Two large numbers gave the highest hit rate (98.3%). Zero large numbers and four large numbers were the hardest (88% and 88%). Each row is 300 targets, so differences of a few points are within sampling noise. The most common shortest route in the sample was 4 steps; boards that needed all six numbers (5 steps) were 20% of the reachable ones. That is why Parsum's easy days have a par of 2 or 3 and its hardest day has a par of 5.
Three example boards, solved with the fewest steps
These boards are in the Parsum style but are not in the game, so working them spoils nothing. The routes are one shortest route each, found by the solver; other routes with the same number of steps may exist.
Board 1: 75, 50, 9, 4, 3, 1, target 336 (par 2)
- 75 + 9 = 84
- 84 × 4 = 336
Board 2: 75, 6, 5, 4, 3, 2, target 418 (par 3)
- 75 − 5 = 70
- 70 × 6 = 420
- 420 − 2 = 418
Board 3: 100, 7, 6, 3, 2, 2, target 381 (par 4)
- 100 − 3 = 97
- 97 × 2 = 194
- 194 × 2 = 388
- 388 − 7 = 381
Habits that help (rules of thumb, not guarantees)
- Look at the target's factors first. If the target is 336 you are looking for a way to make 6 and 56, or 8 and 42. Division by a number you hold is often the last step.
- Combine large numbers early so the small ones can fine-tune: a sum or product of two large numbers is a big stepping stone, and the last step is often a small correction.
- Check one step away. Before anything clever, ask whether some pair already makes the target, then whether some pair makes a number one step from it.
- Use the solver to learn, not to skip. Play first, then paste your board into the solver and compare its route with yours.
The percentages above come from the sample described, not from the TV show, so they will differ a little from published figures; run node tools/stats.mjs in the open-source solver repository to reproduce yours.