1. ## Replacing Numbers

Three identical integers greater than 1 are written on a board. One of the numbers is rubbed off and replaced by a number which is one less than the sum of the other tow. This process is repeated a number of times.

Gerry wants to get the number 2010 from as many starting triples a,a,a as possible. One way of couse is to start with 2010, 2010,2010. What are all the other ways?

Thank you for you help!!

2. 2,2,2
3,2,2
3,4,2
5,4,2
5,6,2
7,6,2
7,8,2
.....
2009,2008,2
2009,2010,2

Note: you should specify that opening integers > 1

3. Thanks bro!

4. Is 2,2,2 the only way to get 2010?

5. Originally Posted by GuMing
Is 2,2,2 the only way to get 2010?
No. Also 8,8,8 and 42,42,42 and 50,50,50 and 288,288,288 ; that's all.

Here's 288:
288,288,288
575,288,288
575,862,288
1149,862,288
1149,1436,288
1723,1436,288
1723,2010,288

6. Thanks!

7. Another problem.
Gemma started with 2,2,2 and tried to get to 17,75,91 but without success. Is it possible to get 17,75,91 from 2,2,2?