Root Sniper Game

A number appears on a plate above a target, and you have a short time to type its square or cube root and fire. The closer your shot, the nearer the bull it lands, and every shot then shows the true root. Each target teaches a little about where roots fall between the squares and cubes you already know.

How to play

1. Choose a level and press START. A card is 10 targets.
2. Find the two whole roots the number sits between. On level 1 that means knowing your squares up to 100².
3. Work out how far along the gap the number is, then type the root to one decimal on the keypad and press FIRE.
4. The shot lands left of the bull when it is too low and right when it is too high. The result shows the true root, how far off you were, and the two powers around the number. Press NEXT for the next target.
5. Each target has a timer. When it runs out, whatever you have typed fires, and a shot with nothing typed is a miss.

For example, take 2,870. It is between 53² = 2,809 and 54² = 2,916, so its root is 53 and a bit. 2,870 is 61 past 2,809 in a gap of 107, a little over half the way, so 53.6 is a good shot. The true root is 53.57.

On a keyboard, type the digits and the point (a comma works too), Backspace takes a digit back, Enter fires and moves on, and Escape or Space pauses. Pausing hides the number, so it cannot buy thinking time.

Scoring

A shot scores by the ring it lands in: 100 for the bull, then 50, 25 and 10, and nothing outside the rings. The rings are distances from the true root, and a shot right on a ring's edge counts for the inner ring.

• Levels 1 and 4: within 0.1 for the bull, then 0.5, 1 and 3.
• Level 2: within 1 for the bull, then 5, 10 and 30. Its roots are ten times bigger than level 1's, so the rings are ten times wider, and the decimal rarely matters.
• Level 3: the exact root for the bull, then 1, 3 and 10.

Shots of 50 or more in a row build a streak. From the fifth shot in a streak each shot scores double, and from the tenth, triple. A miss, or a shot in the 25 or 10 ring, starts the streak again.

For example, on level 1, 53.6 for 2,870 is 0.03 from the true root, a bull worth 100. 53.3 would be 0.27 low, worth 50. If 53.6 were the fifth good shot in a row, its bull would score 200. A perfect card of 10 bulls scores 1,700.

Levels

• Level 1: square roots of 4-digit numbers, 15 seconds a target.
• Level 2: square roots of 6-digit numbers, 25 seconds a target.
• Level 3: cube roots of perfect cubes, with roots from 10 to 99, 10 seconds a target.
• Level 4: cube roots of any number from 1,000 to 999,999, 25 seconds a target.

Level 3 has a trick. The last digit of a cube gives the last digit of its root, because each digit from 0 to 9 cubes to a different last digit: 2 and 8 swap, 3 and 7 swap, and the rest stay the same. The thousands give the first digit. For 389,017, the 7 at the end means the root ends in 3, and 389 is between 7³ = 343 and 8³ = 512, so the root starts with 7. The root is 73.

All four levels are open from the start, and the game remembers the last one you played.

Practice

Turn on practice on the start screen to play without a timer. Before each shot, the message line shows the two powers the number sits between, and on level 3 it spells out the trick. Practice scores are not saved.

Best scores

Your five best scores at each level are kept in this browser, one list per level. Clearing your browser's site data clears them. The list itself is not sent anywhere, but the site's analytics record each finished game, practice games included, with its level, its score and how the shots went.

Roots are a standard event in mental calculation competitions such as the Mental Calculation World Cup and the Memoriad. Read more about mental math, meet some famous mental calculators, or try our other free memory games.