The Boldavian navy has a rigorous training programme. 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, 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 bodies of the dead sharks 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 a cadet’s legs was 14 more than the total number of cadets and the heads of the sharks. 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 a cadet’s 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 cadets and the heads of the sharks. 7 sharks plus 28 cadets equals 35 heads.
Note that although all of the cadets survived yet 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…’
