tough math problem asking for help

Does anyone have any clue as how to solve following math problem?

Find the number of 5-digit numbers less than 40000 in which the 3 3-digit numbers formed by consecutive digits are all divisible by either 17 or 23. Remember, zero cannot be the first digit in a 3-digit number.

Thanks a lot.

 

所有跟帖： 

• 娃在上学，不能试着帮忙。等爱做题的家长来帮你吧：） -怀旧一点点- ♀ (0 bytes) () 11/18/2015 postreply 10:19:59

• 答案是不是不止一个？ -超级机器人- ♂ (451 bytes) () 11/18/2015 postreply 10:43:04

• formed by consecutive digits ? -WISEBAO- ♀ (0 bytes) () 11/18/2015 postreply 10:46:08

• 对啊， abcde， 三个三位数就是abc， bcd， cde， 而不是ade或者其他。 -超级机器人- ♂ (180 bytes) () 11/18/2015 postreply 10:53:24

• Consecutive digits are integers that follow each other in order -WISEBAO- ♀ (0 bytes) () 11/18/2015 postreply 11:04:53

• 如果是这样，那就无解了。不然，就是13个解。 -超级机器人- ♂ (174 bytes) () 11/18/2015 postreply 11:07:46

• 题目问的是有几个 -TZX999- ♂ (158 bytes) () 11/18/2015 postreply 10:54:30

• 码农，程序算的不算 -满墙红叶- ♂ (169 bytes) () 11/18/2015 postreply 10:55:31

• 13 looks right to me. Thanks so much. Can you share how you got -momoftwok- ♀ (0 bytes) () 11/18/2015 postreply 11:15:53

• 我是用程序算的， 算作弊。 就是一个简单的循环（见内） -超级机器人- ♂ (1352 bytes) () 11/18/2015 postreply 11:18:23

• Ha Ha Ha -momoftwok- ♀ (0 bytes) () 11/18/2015 postreply 11:28:52

• 23460=17x23x60 -jenifer- ♀ (0 bytes) () 11/18/2015 postreply 11:04:03

• I used the bruce force and found 8. Hopefully there are smart wa -momoftwok- ♀ (14252 bytes) () 11/18/2015 postreply 11:08:38

• 题中给定的17和23是两个素数，素数有很多特别性质 -TZX999- ♂ (74 bytes) () 11/18/2015 postreply 11:15:43

• Count by Cases. -dr_yin- ♂ (738 bytes) () 11/18/2015 postreply 17:30:05