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Assume (x1,y1) , (x2,y2), (x3,y3) are the ranges of the three coke machines.
- ramsundargovindarajan February 17, 2013You have a range (m,n).
As stated before, m < X < Y < n for some (X,Y) to be obtained by a linear combination of the three machines.
Which means K1*x1 + K2*x2 + K3*x3 (= X) > m and K1*y1 + K2*y2 + K3 * y3 (=Y) < n
Take the second equation , we need to find all (K1,K2,K3) < n Start from n-1 (assume everything is an integer here. If not then we can scale the numbers till they become integers).
For every (k1,k2,k3) which satisfies the second equation see if it also satisfies the first equation. If yes , the problem can be solved . If no, decrement Sigma Ki*Xi to n-2 and repeat the algorithm.
It is a brute force approach almost. But it solves definitely.