AMC 8 1993 Problem 24
AMC8 1993 年第 24 题
数列与规律★★★★☆
What number is directly above 142 in this array of numbers?
在此数字阵列中，142 正上方的数是多少？
- A.99
- B.119
- C.120
- D.121
- E.122
正确答案 · Correct Answer
C
解析 · Solution
解法1
常规解法 · 行差 + 行容量
第 行的数比正下方的数小 ；前 行共 个数。因 ，142 在第 12 行（是 144 前面第 2 个）。它正上方在第 11 行，小 2×11=22，即 142-22=120。
巧解 · 每行末是平方数
每行个数为奇数、而奇数之和是平方，故每行末尾都是完全平方数。第 12 行末 144、第 11 行末 121；142 是第 12 行倒数第 2 个，正上方比 121 小 1，即 120。
Solution 1
Elementary · row differences + row capacity
A number in row is less than the one directly below it, and rows 1 through contain numbers. Since , the number 142 is in row 12 (two before 144). The number directly above is in row 11, which is 2×11=22 less: 142-22=120.
Slick · each row ends in a square
Each row ends in a perfect square (each row has an odd count of entries, and sums of consecutive odd numbers are squares). Row 12 ends at 144 and row 11 at 121; since 142 is the second-to-last entry of row 12, the entry directly above it is one less than 121, namely 120.
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