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Three Bricklayers (Posted on 2013-06-21) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 3 of 4 |

We can assume no bricklayer can lay more than 200 bricks per minute. Also assume all workers take up the full time and none finishes even a minute or fraction of a minute before any other.

DECLARE FUNCTION gcd# (a#, b#)
DECLARE FUNCTION lcm# (a#, b#)
DEFDBL A-Z
min = 9999999
FOR a = 1 TO 198
FOR b = a + 1 TO 199
FOR c = b + 1 TO 200
 ab = a + b: ac = a + c: bc = b + c
 abc = a + b + c
 sz = lcm(a, lcm(b, lcm(c, lcm(ab, lcm(ac, lcm(bc, abc))))))
 IF sz / a <> sz / bc AND sz / b <> sz / ac AND sz / c <> sz / ab THEN
    IF sz <= min THEN
      min = sz: mina = a: minb = b: minc = c
      PRINT a; b; c, sz
    END IF
 END IF
NEXT
NEXT
NEXT

FUNCTION gcd (a, b)
 x = a: y = b
 DO
  q = INT(x / y): r = x - y * q
  IF r = 0 THEN gcd = y: EXIT FUNCTION
  x = y: y = r
 LOOP
END FUNCTION

FUNCTION lcm (a, b)
 lcm = a * b / gcd(a, b)
END FUNCTION

finds:

  speeds      bricks
 1  2  4       420
 1  3  5       360

So 360 is the smallest number of bricks.

Edited on June 21, 2013, 1:01 pm
  Posted by Charlie on 2013-06-21 12:59:55

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