Max starts on his way to Pewter Town, for the first Gym Battle. On the way, he bumps into a mysterious man offering a chance at catching loads of Pokémon. “What do I need to do?” asks Max. The mysterious man replies “Here’s a map of Viridian Forest. You will begin at (8,10). Every grid has an unique Pokémon. But if your position is (a,b), you can only move to `(a,a+b), (a,a-b), (a+b,b), (a-b,b), (b-a,b)` and `(a,b-a)`. You can continue until you have no Pokémon under your reach.” What is the sum of digits of the maximum number of Pokemons Max can catch?

Explanation

This is based on the fact that HCF or GCD of (a,a-b) or (a-b,b) is the same that of (a,b). This Follows from the fact that every mutual factor of a and b are also the factor of a+b and |a-b|.
And so becomes the grid. This will happen at each stage of reach for some (a,b), Thus lion can only reach those points whose gcd or hcf is (8,10)==2, Therefore the answer is all the coordinates whose hcf is 2,
`{(2,2)}** 1`
`{(2,4)(4,6)(6,8)(8,10)(10,12) (2,6)(6,10) (2,8)(4,10)`
`(2,10)(2.12)}**2` (As these could be both a,b and b,a)