Groeipatroon

A growing pattern (groeipatroon): figure 1, 2, 3 of tiles or matches, each a
bit bigger than the one before. The pupil works out how many tiles a later
figure has (`ask`), or which figure has a given number (`find`, reasoning
backwards). The booklet draws the figures; the answer sheet has a box per
question. Graded per box. The teacher manual works each answer out from the
structure of the figure ("1 in the middle and 4 arms of 10: 1 + 4 × 10"),
not only by counting on.

| `shape` | Figure n | Growth |
| --- | --- | --- |
| `l` | an L of tiles | 2n + 1 |
| `plus` | a plus with arms of n | 4n + 1 |
| `t` | a T: 2n + 1 on top, a leg of n | 3n + 1 |
| `pool` | tiles around a pool of n | 2n + 6 |
| `fence` | n squares of matches in a row | 3n + 1 |
| `triangles` | n triangles of matches in a row | 2n + 1 |
| `staircase` | a staircase 1 + 2 + … + n | n(n + 1) / 2 |
| `square` | an n × n square | n × n |
| `rectangle` | an n × (n + 1) rectangle | n × (n + 1) |

`show` (2 to 4, default 3) is how many figures are drawn; `counts: true`
prints the number under each. Asking about a drawn figure is an error, and so
is a `find` number no figure has (the message gives the nearest ones).

Easier: `counts: true`, ask about the next figure only. Harder: ask about
figure 10 or 20, add `find`, or take a quadratic pattern (staircase, square,
rectangle). Let the pupil draw figure 4 in a separate `drawing` task first.

```yaml
- type: task
  id: q1
  prompt: Hoeveel tegels hebben deze figuren?
  answer:
    type: tempono/growing-pattern@1.0.0
    shape: plus
    ask: [ 4, 10 ]
    find: [ 41 ]
```