AMC 8 2024 Problem 4
AMC8 2024 年第 4 题
特殊数与不定方程★☆☆☆☆
When Yunji added all the integers from 1 through 9, she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?
Yunji 将 1到 9之间的所有整数相加时，漏加了一个数字，得到的错误结果是一个平方数。请问Yunji 漏加的是哪个数字？
- A.5
- B.6
- C.7
- D.8
- E.9
正确答案 · Correct Answer
E
解析 · Solution
解法1
基本上下面的那个我想只是解释得稍微不同。所以是的，我们加1得到45。然后我们看到最近的平方数，显然是36（希望我们都记住了平方数），然后我们用45减去36得到 9 。把数字1到9相加得到45。这是她预期的和，但她得到的是一个完全平方数。因为她得到了那个完全平方和，这个和小于45。比45小的平方数是36。所以45=9。所以答案是9。
Solution 1
basically the one below i guess just explained a lil different. so yes we add 1 to get 45. then we see what's the closet square, which is obviously 36 (i hope we have our squares memorized ) and then we do 45 minus 36 to get 9. Adding numbers 1 through 9 gives us 45. This was her expected sum, but what she got was a perfect square. Since she got that perfect square sum a number, that sum is less than 45. The square number right under 45 is 36. So 45 = 9. So the solution is 9.
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