Design & Technology

To get the right combination.. June 26th, 2008

By Chil-Young Kwon
Production Management Team
Kia Motors Corporation

How can we arrange the 18 balls in the box below to get four blue balls while satisfying the designated rules?

This may seem like a random mathematical puzzle; however, such logical thinking is an essential attribute for line managers. In an earlier piece, we mentioned that the genetic makeup of the car body is already decided when it enters the assembly line. The makeup affects the order in which the bodies enter the line. That is, the input sequence can be affected by such rules as the “impossible sequences” noted in the figure above. This is referred to as input rules at the plant. Even just a few conditions can complicate things as you will see when you try to solve the puzzle.


The input rules have to take into account many factors. The main reason for that is the work hours required. For example, an LPG vehicle cannot be deployed in succession because they need considerable time for assembly. Cars for RHD nations also cannot pass through in succession because the line workers’ places have to be switched. There could be many rules to satisfy when assembly codes are similar, when a car with new specifications enters the line, and in factories that produce more than two model types. At Kia plants, we use sequences that comply with input rules for timely production and delivery of ordered vehicles.

Well, how would you solve the puzzle? I found an answer which is written in the box below. If you find a better solution, please let me know!!


  • It seems to me the solution is incorrect, based on the rules provided. It states 1 must out number 2 in a ratio of 2:1 therefore there must be ten 1’s if you have five 2’s. Your running sequence is 213121312131213121,
    totalling 18 balls there are only nine 1’s and five 2’s leaving you one 1 short. try taking 18 and divide it by 2 plus 1 that will give you your 1 basis and you 2 is half that number, with 3 being the odd one out 10-5-3 or 8-4-6. Interesting problem, to have.

  • It says can be in sequence 2 -3 but doesnt say 3-2 or 2-1 or 1-2
    so can you run the sequence like this 1321321 313121313 21
    there are no 2-3 no double 1-1, and there are eight 1’s and four 2’s, and six 3’s. there are lots of combination that work, but interpreted the way you have the mathematics is impossible because you have many 1-2 sequence. Let me know what the outcome is please.

  • As I understand the design rules there need to be at least four 2’s and therefore at least eight 1’s. Then of course you need to minimize the number of 3’s.
    I found this combination to be the shortest:
    121 3 121 3 121 3 121
    Look how the three 3’s separate the four 121’s