A small company with three bricklayers is hired to build a barbecue. Each worker can lay a certain integer number of bricks per minute. The company could assign any combination of 1, 2 or all 3 workers to the job, and each combination would complete the barbecue in a different integer number of minutes.

What is the minimum number of bricks in the barbecue?

This doesn't change the ultimate answer of the minimum, as that doesn't change, but lists all the reasonable possibilities: no bricklayer can lay more than a brick per second; even the slowest worker can finish in an 8-hour day and there are fewer than 1000 bricks in the barbecue:

 speeds      bricks
1  2  4       420
1  3  5       360
1  6  14      420
2  3  10      780
2  4  8       840
2  6  10      720
2  12  28     840
3  5  7       840

Posted by Charlie on 2013-06-21 13:13:57