A permutation and combination problem

  • #1
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.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is

(1) 901 (2) 861 (3) 820 (4) 780

my attempt:
for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
 

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  • #2
andrewkirk
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for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
No, the sum must be less than or equal to 41. How would you count the points in that triangle?
 
  • #3
No, the sum must be less than or equal to 41. How would you count the points in that triangle?
yes it should be less than 41,changed.sorry
 
  • #4
haruspex
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yes it should be less than 41,changed.sorry
Yes, less than, not less or equal. Likewise what are the minimum x and y values?
To solve the question, can you think of a region for which:
- the number internal points is much easier to count, and
- there is a fairly straightforward relationship between its internal point count and that of your triangle?
 

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