Is it possible to complete the following expression
2****9=2009
and make it true by replacing two asterisks with a selection of the four operational symbols (+,-,x ,/) and two other asterisks with digits 0,1 .....9? Operational symbols and digits can be the same. Explain why .
急,一條數學難題,高手請進,20點
2009-06-01 4:03 am
回答 (3)
2009-06-01 9:37 am
✔ 最佳答案
2009的因式分解為7*7*41而您給的題目最大數值為29*9*9=2349
如題所說，需要兩個數字兩個符號。
所以不足以湊成因式分解的數字，
吾想過湊成2000最後再加上9，
但是也因為題目的限制無法完成，
所以這題答案應為無法完成。
參考: 計算機及自己
2009-06-06 2:01 am
The operation symbols cannot be next to each other, therefore the combinations can only be one of the following three (? is operation symbol, # is digit):
2?#?#9 ...(1)
2?##?9 ...(2)
2#?#?9 ...(3)
Obviously the biggest numbers contained in the expressions can only be 2 digit numbers.
+, - or / cannot help to make up the 4 digit number 2009. Therefore the operation symbol must be x.
First line is even as it starts with "2 x ..."
The rest two must be multiple of 9 as they end with "... x 9"
Both are not possible as 2009 is not even and is not a multiple of 9.
2?#?#9 ...(1)
2?##?9 ...(2)
2#?#?9 ...(3)
Obviously the biggest numbers contained in the expressions can only be 2 digit numbers.
+, - or / cannot help to make up the 4 digit number 2009. Therefore the operation symbol must be x.
First line is even as it starts with "2 x ..."
The rest two must be multiple of 9 as they end with "... x 9"
Both are not possible as 2009 is not even and is not a multiple of 9.
2009-06-01 7:24 am
The maximum we can get is by replacing two asterisks with x, and the other two with 99, that is 2x99x9=1782
So, I think it is impossible to complete the expression.
So, I think it is impossible to complete the expression.
收錄日期: 2021-04-23 23:20:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090531000051KK01774