Rules
Formula Archery was the death match of the first round of University War. Two teams combined their number cards into four digits and raced to make the numbers printed on an archery target.
The target
The target has five rings. From the centre out: yellow (5 points), red (4), blue (3), black (2) and white (1). Each ring holds several numbers.
Shooting
- Make a formula that uses each of the four digits exactly once. You can use + − × ÷, powers (^), square roots (√), factorials (!) and brackets as often as you like.
- The formula’s value is where your arrow lands: it hits the number on the target with that value.
- You score that ring’s points. Each number can only be hit once.
- Hitting three neighbouring numbers in the same ring earns a bonus of 2 points.
- The first to 25 points wins.
Our version
- The four digits are drawn at random from 1 to 9 and stay the same for the whole game.
- The target has 27 different numbers: 3 yellow and 6 in each other ring. They are placed by difficulty: white and black numbers can be made with + − × ÷ alone, blue numbers are bigger, red numbers need a power and yellow numbers need a square root or a factorial.
- Digits cannot be joined into bigger numbers. The final value must be a whole number, but steps in between can be fractions, as in 7 ÷ 2 × 4 + 1.
- A formula that breaks the rules is refused with no penalty. On your own, a valid formula that misses every open number counts as a miss but costs nothing.
- vs AI: you and the AI shoot at the same target. The AI is slower on the inner rings and on easier levels. The match ends at 25 points, when every number is hit, or after 10 minutes.
- Daily and Practice: reach 25 points as fast as you can.
- Live value: with this setting on (the default), the value of your formula shows as you type.
Strategy
Take the bonus. Three neighbours in one ring give 2 extra points. The three yellow numbers together are worth 17.
Learn the tools. 3! is 6, 4! is 24, √9 is 3 and 2^5 is 32. A factorial or a power often turns a small number into exactly the size you need.
Use 1 as a spare. Multiplying or dividing by 1, or raising to the power of 1, lets you use up a digit without changing anything.
Work backwards. For 47, think 48 − 1 or 7² − 2, then check whether the digits you have left fit.