### Brain Teasers

# Sharks 2

The Boldavian navy has a rigorous training program. In order to graduate from the naval academy, cadets must enter a pool and fight sharks. Today, a group of cadets was tested. Each cadet put on his mask, snorkel, and two flippers; and armed himself with a knife. Then the cadets jumped into the pool. The sharks were then released from their pens. After 10 minutes of gruelling hand-to-fin combat, all of the sharks were killed. Miraculously, none of the cadets were killed. Exiting the pool, the cadets began to haul the shark bodies out of the water. The dead sharks were soon lying in a row. One of the cadets noted that during the fight, there were 4 times as many cadets in the water as there were sharks. A second cadet then stated that the number of legs they now had was equal to the square of the number of sharks. A third said that the number of cadet legs was 14 more than the total number of cadet and shark heads. How many sharks were killed?

### Answer

7 sharks were killed.Since there were 4 times as many cadets, there were 28 cadets. The number of cadet legs is equal to the square of the number of sharks, which would be 49 legs. 49 legs is 14 more than the number of cadet and shark heads: 7 sharks plus 28 cadets equals 35 heads.

Note that although all of the cadets survived, nothing was said about possible injuries. In fact, each shark had bitten off one leg from each of 7 cadets. This explains the shortage of legs, since 28 cadets should have had 56 legs, not 49. Also note the statement of the second cadet, who said 'the number of legs they NOW had ...'.

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