# Pinewood Derby Chart (#56) **URL:** \ **Category:** Ruby\ **Created:** [November 25, 2005, 8:13pm UTC](https://www.ruby-forum.com/t/pinewood-derby-chart-56/48859 "2005-11-25T20:13:21Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![bbazzarrakk](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/b/47e85d/32.png) [@bbazzarrakk](https://www.ruby-forum.com/u/bbazzarrakk)\ **Post date:** [November 25, 2005, 8:13pm UTC](https://www.ruby-forum.com/t/pinewood-derby-chart-56/48859/1 "2005-11-25T20:13:21Z")
The three rules of Ruby Q.: 1. Please do not post any solutions or spoiler discussion for this quiz until 48 hours have passed from the time on this message. 2. Support Ruby Q. by submitting ideas as often as you can: [http://www.rubyquiz.com/](http://www.rubyquiz.com/) 1. Enjoy! -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= by Bob S. I was a Cub Scout leader for five years and one of our favorite activities was the annual Pinewood Derby. For you non-Scouts, this is a competition between small gravity-powered cars made by the boys using standard kits containing a wood block, plastic wheels, and nails for axles. The cars compete against each other down a sloping, multi-lane track (2-6 lanes is typical) about 30 feet long. Some Cub Scout packs use a “ladder” elimination system for their derby, but this isn’t much fun for the boys that are eliminated early. Much more enjoyable is a “round-robin” approach that lets each boy’s car run in the same number of heats, racing against different opponents each time. You can find links to more Pinewood Derby information at: ``` http://members.aol.com/StanDCmr/pwportal.html ``` This week’s task is to create a Ruby program to generate a chart for a Pinewood derby. In order to make the event fair, each car should be scheduled into each lane of the track the same number of times (to compensate for any lane differences due to track imperfections.) We’ll use the term “round” to refer to each car running once in each lane. The input to your program will be: ``` Number of cars Number of lanes Number of rounds ``` For example, let’s assume we have 25 cars and a 4-lane track. If we want each car to run twice in each lane (2 “rounds”), that means: ``` Number of rounds: 2 Number of runs per car: 2 rounds x 4 lanes = 8 Total number of runs: 8 runs/car x 25 cars = 200 Total number of heats: 200 / 4 lanes = 50 heats ``` So we have to come up with a chart that assigns the cars to lanes and heats. If we number the lanes from 1 to 4 and the cars from 1-25, our chart might look something like this: ``` Heat Lane 1 Lane 2 Lane 3 Lane 4 ---- ------ ------ ------ ------ 1: 9 2 13 10 2: 12 8 5 21 3: 16 19 6 4 ...and so on ``` The trick is to create a chart that is as fair as possible. A “perfect” chart would be one in which: ``` 1) Each car runs in the same number of heats 2) Each car runs in each lane an equal number of times 3) Each car runs against every other opponent an equal number of times 4) The heats a car is assigned to are evenly spread throughout the ``` event. (In other words, a boy shouldn’t run in the first 8 heats and then have to sit out for the rest of the event.) In practice, you cannot create a perfect chart for all combinations of inputs. For instance, if we ran just one round with our 25 cars, each car would run in 4 heats and face 12 opponents (3 opponents per heat). Since there are 24 opponents, it isn’t possible to face all the opponents equally. But you would want to try to maximize the number of opponents faced, rather than having two cars face each other several times. You may want to create a function to evaluate your chart against the criteria above, so you can rank charts as to their “quality”. ---
**Author:** ![bbazzarrakk](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/b/47e85d/32.png) [@bbazzarrakk](https://www.ruby-forum.com/u/bbazzarrakk)\ **Post date:** [November 28, 2005, 10:46pm UTC](https://www.ruby-forum.com/t/pinewood-derby-chart-56/48859/2 "2005-11-28T22:46:32Z")
The core of my solution is at: [http://users.adelphia.net/~showaltb/rubyquiz/56/derby.rb](http://users.adelphia.net/~showaltb/rubyquiz/56/derby.rb) It assigns cars by computing a “weight” factor for each car based on the following criteria: a) How many times has the car been assigned to this lane? b) How many times has the car been matched up against the opponents already slotted to this heat? c) How long has it been since the car was last scheduled to a heat? The weight factors act as a bias against selecting a car. ---
**Author:** ![bbazzarrakk](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/b/47e85d/32.png) [@bbazzarrakk](https://www.ruby-forum.com/u/bbazzarrakk)\ **Post date:** [November 30, 2005, 6:02am UTC](https://www.ruby-forum.com/t/pinewood-derby-chart-56/48859/3 "2005-11-30T06:02:05Z")
On Nov 28, 2005, at 3:43 PM, Bob S. wrote: > c) How long has it been since the car was last scheduled to a heat? > > The weight factors act as a bias against selecting a car. I dig any Ruby program with a class called ChaoticChart! Seriously, this is a very interesting solution to read. Must by why you scared all the others off. You just can’t compete with true chaos. 😉 James Edward G. II