# On a straight line 100,100 points are located. The sum of distances from the first at the left from them to all others is equal 2017, and the sum of distances from the second at the left to all others (including the most left) is equal 1625. What the distance between the first and second points is equal at the left to?

Vatavtyul

65

In total points 100. The sum of distances is from 1 points to the others: S1 = A1A2 + A1A3 + A1A4 +... + A1A100 = the Sum of distances is 2017 from 2 points to the others: S2 = A2A1 + A2A3 + A2A4 +... + A2A100 = 1625 But distance of A1A3 = A1A2 + A2A3, because they on one straight line. And too most all other points: A1A100 = A1A2 + A2A100. Therefore S1 = A1A2 + A1A2 + A2A3 + A1A2 + A2A4 +... + A1A2 + A2A100 = = 99*A1A2 + (A2A3 + A2A4 +... + A2A100) = 98*A1A2 + Is received by S2 98*A1A2 + 1625 = 2017 A1A2 = (2017 - 1625)/98 = 4

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