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Elementary school mathematics competition questions
1, solution: by enumeration:

The time when the snail arrives at point A is:

6、6+7= 13、 13+8=2 1、2 1+9=30、30+ 10=40、40+ 1 1=5 1、5 1+ 12=63、63+ 13=76、76+ 14=90、……

The time for earthworms to reach point A is as follows:

5、5+9= 14、 14+ 13=27、27+ 17=44、44+2 1=65、65+25=90、……

It can be seen that when the time is 90 minutes, snails and earthworms reach point A at the same time.

2, enumeration method:

Divide by 9 first, and see if the remainder can be divisible by 3 or not.

207÷9=23 2+3=5 (not divisible by 3)

2007÷9=223 2+2+3=7 (not divisible by 3)

2007 ÷ 9 = 2223 2+2+2+3 = 9 (divisible by 9)

200007 ÷ 9 = 22223 2+2+3 =11= 2 (not divisible by 3)

200007 ÷ 9 = 222223 2+2+2+3 =131+3 = 4 (not divisible by 3).

2000000007 ÷ 9 = 2222223 2+2+2+3 =151+5 = 6 (divisible by 3 but not by 9).

It's 20000007.