Question

数学答案是什么

POW #12 – Another Special Number Isn’t it sad that the famous numerologist Could never find the first special number that was so easy for you? Well, don’t get too big-headed over your first success in the number creation business. Many would be numerologists have tasted victory in their first attempt only to be disappointed the very next time. Let’s see how good you are. Here is a number which Eluded numerologists for hundreds, maybe thousands of years. See if you can find it: •It has ten digit •It contains the digits 0-9 •Its first 2 digits are divisible by 2 •Its first 3 digits are divisible by 3 •Its first 4 digits are divisible by 4 •This pattern continues all the way through the number.

Answer 1

共十个数字，0-9.
前两位可被2整除，前3位可被3整除，前4位可被4整除，类推，求此数
由前5个数字组成的数能被5整除,说明第5个数字是5或者0
由前10个数字组成的数能被10整除,说明第10个数字是0,则第5个数字是5.
已知可推出偶数位为偶数,
由前4个数字...4..,说明第3和第4个数组成的数能被4整除,可推出第4个数字为2或者6
由前8个数字...8..,说明第6,7,8组成的数能被8整除,可推出第6位为4或8,第7位为1或者9,第8位为6,则第4位为2或者第7位为3,7,第8位为2,则第4位为6
当第8位为6,第4位为2时
前3位能被3整除,前6位能被6整除,说明4~6位能被3整除,则258合适,第6位为8,第2位为4
前3位能被3整数,说明为147或741,则第7位为9,则第9位为3
前7位被7整除不成立.
当第8位为2,第4位为6时
前3位能被3整除,前6位能被6整除,说明4~6位能被3整除,则第6位为1,4,7只有4符合题意(偶数位为偶数)
则第2位为8
前3位能被3整数,说明为381,183,789,987,189,981
可得原数为3816547290,1836547290,7896543210,9876543210,1896543270,1896547230,9816547230,9816543270
前7位可被7整除,说明3816547290合适