51. A teacher assigns each of her 18 students a different integer from 1 through 18. The teacher forms pairs of study partners by using the rule that the sum of the pair of numbers is a perfect square. Assuming the 9 pairs of students follow this rule, the student assigned which number must be paired with the student assigned the number 1 ?

Answer and Explanation

Your Answer is

Correct Answer is B

Explanation

The question stem says that the sum of the numbers of all 9 groups of students is a perfect square number. The perfect square numbers that can be obtained by adding two pairs of 1-18 are: 4, 9, 16, 25. Therefore, 18 must be matched with 7, 17 must be matched with 8, and 16 must be matched with 9. At this time, 15 has two choices, one is to match with 10, and the other is to match with 1. If 15 matches with 10, then 6 cannot match with 10, but can only match with 3, then there is no number that can match with 1 at this time. So 15 must match 1.