Countdown number probabilities
The numbers game uses four large numbers and twenty small-number tiles.
The large numbers are:
25, 50, 75, 100
The small numbers are two copies of each number from 1 to 10:
1, 1, 2, 2, 3, 3, ..., 10, 10
Choosing the large numbers
In numbers practice, choosing 0, 1, 2, 3, or 4 large numbers fixes how many large numbers will be drawn. The selected large numbers are
drawn without replacement from 25, 50, 75, and 100, so there can never be duplicates.
If you use the Random button, the number of large numbers is chosen uniformly from 0 to 4. The daily numbers puzzle uses the same rule.
| Large count | Probability with Random/daily |
|---|---|
| 0 | 20% |
| 1 | 20% |
| 2 | 20% |
| 3 | 20% |
| 4 | 20% |
For a fixed large count, each individual large number has probability large count / 4 of appearing. With Random/daily, the average large count is 2, so
each of 25, 50, 75, and 100 appears with probability 50%.
Choosing the small numbers
After the large numbers are chosen, the rest of the six-number selection is filled with small numbers. Small numbers are drawn without replacement from the twenty-tile small-number stack.
For a particular small value, such as 7, there are two copies in the stack. The chance that at least one copy appears depends on how many small tiles are
needed:
| Large count | Small tiles drawn | Chance a specific small number appears |
|---|---|---|
| 0 | 6 | 52.11% |
| 1 | 5 | 44.74% |
| 2 | 4 | 36.84% |
| 3 | 3 | 28.42% |
| 4 | 2 | 19.47% |
With Random/daily, averaging over the five possible large counts, a specific small number from 1 to 10 appears at least once with probability 36.32%.
It appears exactly once with probability 32.63%, and twice with probability 3.68%.
Choosing the target
The target is chosen uniformly from 101 to 999, inclusive.
There are 899 possible targets, so each target has probability 1/899, or about 0.11%.
The target is chosen independently of the six numbers. The practice page briefly animates random targets before showing the real one, but the final target is still just a uniform random number from 101 to 999.