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There is a monkey which can walk around on a planar grid. The monkey can move one space at
a time left, right, up or down. That is, from (x, y) the monkey can go to (x+1, y), (x-1, y), (x, y+1),
and (x, y-1). Points where the sum of the digits of the absolute value of the x coordinate plus the
sum of the digits of the absolute value of the y coordinate are lesser than or equal to 19 are
accessible to the monkey. For example, the point (59, 79) is inaccessible because 5 + 9 + 7 + 9
= 30, which is greater than 19. Another example: the point (-5, -7) is accessible because abs(-5)
+ abs(-7) = 5 + 7 = 12, which is less than 19. How many points can the monkey access if it starts
at (0, 0), including (0, 0) itself?

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1 mathematical challenge_problem

  • 1. There is a monkey which can walk around on a planar grid. The monkey can move one space at a time left, right, up or down. That is, from (x, y) the monkey can go to (x+1, y), (x-1, y), (x, y+1), and (x, y-1). Points where the sum of the digits of the absolute value of the x coordinate plus the sum of the digits of the absolute value of the y coordinate are lesser than or equal to 19 are accessible to the monkey. For example, the point (59, 79) is inaccessible because 5 + 9 + 7 + 9 = 30, which is greater than 19. Another example: the point (-5, -7) is accessible because abs(-5) + abs(-7) = 5 + 7 = 12, which is less than 19. How many points can the monkey access if it starts at (0, 0), including (0, 0) itself?