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March 26, 2017

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How many ordered pairs of integers (x,y) are there that satisfy |x|+|y| ≤ 10?

  • Math (Algebra) - ,

    160

  • Math (Algebra) - ,

    from (0,10) to (0,-10) -- 21
    from (1,9) to (1,-9) --- 19
    from (2,8) to (2,-8) --- 17
    ..
    from (9,1) to (9,-1) -- 3
    and (10,0) ----- 1

    same thing on the left side, but we can't count the centre line twice, so
    sum = 2(1+3+5+...19) + 21
    there are 10 terms in the series
    sum = 2(5)(first + last) + 21
    = 10(20) + 21 = 221

    or 2(1+3+5+..+21) - 21
    = 2(11/2)(1 + 21) - 21 = 221

    There are 221 such ordered pairs.

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