ABCD(是不知名的四位數)乘以9,等於CDBA,想求A=?,B=?,C=?,D=?(請列式!)
(夲人對奧數一竅不通,只是代姪女問),Thanx!!!!!
有奥數問題一問,請各位奥數高手指教一下?!
2006-10-15 5:09 am
回答 (2)
2006-10-15 5:30 am
✔ 最佳答案
abcd * 9 = cdbaabcd is a4-digit number
=> a>=1,
=> 10000 > cdba > a000*9=9000
=> c=9 and a=1
=> abcd = 1b9d
a=1 and (9d mod 10) = a
=> d = 9
=> 1b99
abcd * 9 < 10000,
=> bcd * 9 < 1000
=> b = 0 or 1
but 1099 * 9 = 9891 <> 9901 and 1199 * 9 =10791 <> 9911
=> No solution
2006-10-15 5:19 am
無解！你打錯題目！
ABCD*9=CDBA
because ABCD *9 <10000 therefore A=1,
then 1BCD*9>=9000 therefore C = 9
because the unit digit of D*9 is 1 therefore D=9
1B99*9=9891+B*9*100=CDBA, (98+9B)*100 +91 = CD*100 + BA therefore B=9
but 1999*9 = 17991 >10000 contradiction
THERE ARE NO SOLUTION FOR THIS QUESTION!!!
You may have mistype some part of the question.
ABCD*9=CDBA
because ABCD *9 <10000 therefore A=1,
then 1BCD*9>=9000 therefore C = 9
because the unit digit of D*9 is 1 therefore D=9
1B99*9=9891+B*9*100=CDBA, (98+9B)*100 +91 = CD*100 + BA therefore B=9
but 1999*9 = 17991 >10000 contradiction
THERE ARE NO SOLUTION FOR THIS QUESTION!!!
You may have mistype some part of the question.
收錄日期: 2021-04-12 22:51:45
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https://hk.answers.yahoo.com/question/index?qid=20061014000051KK05591