Curious George's Adventures On The Coordinate Plane

Curious George plays around on a planar grid. George can move one space at a time: left, right, up or down.

That is, from \((x, y)\) George can go to \((x+1, y)\), \((x-1, y)\),\( (x, y+1)\), or \((x, y-1)\).

George can access any point \((x,y)\) where the sum of the digits of \(|x|\) \(+\) the sum of the digits of \(|y|\) is \(\leq 19\).

How many points can George access if he starts at \((0,0)\) including \((0,0)\) itself?

Explicit Examples

  • \((59, 79)\) is inaccessible because \(5 + 9 + 7 + 9 = 30\), and \(30 > 19\)
  • \((-5, -7)\) is accessible because \(|-5| + |-7| = 12 \leq 19\)
  • \((190,90)\) is not reachable, considering its neighbors are all not reachable.
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