Date: Mon, 9 Aug 1999 18:40:33 -0600 (CST)
Name: Brad
Who is asking: Student
Level: Secondary

Question:
Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2.
Express N as the product of four integers, each of them greater than 1.

Hi Brad
One problem solving technique that works here is to try a similar but smaller problem. With this problem I decided to try N = 111222.

111222 = 111000 + 222 = 111(1000) + (111)2 = 111(1002)

1002 is clearly divisible by 2, but it is also divisible by 3. (A useful fact about integers is that an integer is divisible by 3 if and only if the sum of its digits is divisible by 3.) Hence 111222 = 111x2x3x167.

Now try 111...1222...2.

Cheers
Penny

 

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