The objective of the Battle Royale Coinsort competition is to build a device that is
capable of sorting a mixture of different kinds of wooden dowel “coins” into three bins.
Teams are expected to maximize the sorting accuracy of their device
while keeping costs to a minimum.

These items are shown in the photograph above. The coins have the following nominal dimensions:

1. Red: 1″ diameter and 1/4″ thickness
2. White: 1″ diameter and 5/32″ thicknes
3. Black: 1″ diameter and 5/32″ thickness

The sorting bins are round 745 mL reusable containers. They have nominal outer dimensions of 3.5″ in height and 5.5″ in diameter.

Construction

Each device must be constructed according to the following rules:

1. The device must be self-supporting. No human intervention can be used to hold or stabilize the device. Adhesives may not be used to affix the device to the table. The maximum footprint for the device is 23” by 29”, which represents the limits of the table top on which testing will take place.
2. The device must have a base that remains stationary on the table top. The device may not be picked up to be operated.
3. In order to reduce human involvement in the sorting process, the device must be operated using only a single action. It may either be a one-time or a continuous action. For example, flipping a switch or hitting a start button would also count as a single, one-time action. Turning a crank would count as a single continuous action. Combinations of two or more of these, or other actions, will not be permitted.
4. Shaking will be permitted as an action, provided that rule (2) is observed and the agitation occurs only in a single axis as a continuous action.
5. The device must have three areas in which the three plastic containers may be inserted or supported. The coins must be sorted into these three containers. Insertion/removal of the containers must all be done from one side of the device.
6. The following power sources are not permissible: compressed gas canisters, chemicals, explosives. Electricity will be permitted provided batteries are used; wall outlets or other sources of electricity are not allowed.
7. ALL valid parts must be sourced from Canadian suppliers and be accompanied by a link to a Canadian website which lists the price in Canadian dollars. For the purposes of this competition, a Canadian website must have a “.ca” domain (e.g, <http://www.lowes.ca>, <https://www.thesource.ca>). Presence of any non-standard parts will result in disqualification.
8. Items need not be purchased from the supplier listed; however, they must have a Canadian supplier as described above.

Cost

The cost of the device is determined as follows:

1. Costs must be calculated using the list price an official website, regardless of the actual purchase price.
2. Item costs and calculations should be reported to the nearest penny (i.e., two decimal places).
3. All taxes should be excluded from calculations.
4. Where items are sold in packages of two or more, the item cost may be calculated as a fraction of the total. For example, ¾” #10 wood screws are sold in packages of 75 for $4.57. Therefore, the cost of three screws is (3/75)$4.57=$0.18 after rounding to the nearest penny).
5. The cost of wood or other material may be scaled based on the number of useable parts that could be machined from a given raw piece of material.
6. Costs of consumables such as tape or glue may also be prorated based on the length or mass of material used.
7. The costs of tools should NOT be included in the analysis.

Performance

Performance is evaluated as follows:

1. Prior to testing, each team will be required to submit an itemized cost analysis of all the parts used in their device.
2. Testing will take place in F-228 on a small table with nominal surface dimensions of 23” by 29”.
3. The device will be photographed and visually compared against the parts listed in the cost analysis. No changes may be made to the device after this point.
4. The three plastic containers will be inserted into the device.
5. A mix of 10 to 15 coins will be dumped into the device by the instructor. This will be done from a container identical to the plastic containers into which sorted coins will be placed. The exact total, or number of each type of coin, will not be known in advance; however, there will be at least two coins of each type.
6. Once the coins have been dumped into the device, each team will have 5 minutes (300 seconds) to complete the sorting.
7. Team members may not interact with their device in any way during testing, other than using the single action. This means that the device may not be altered, repaired, or unclogged.
8. The three containers will be removed following the sorting and points will be awarded as described above.
9. Problems or issues not expressly covered by these rules may be treated or penalized at the discretion of the instructor.

Scoring

Two rounds of testing are performed using two iterations of the design: a prototype round, and a final round. Scoring during the prototype round is relative, whereas the final round testing is an absolute scoring system determined based on the prototype results. In both rounds the total score is based on a weighting of 70% for performance and 30% for cost.

The performance of the device is assessed based on its accuracy. Coins correctly sorted are given a point. Coins incorrectly sorted, or not sorted at all, result in a point being subtracted. The accuracy is calculated as the total points normalized by the total number of coins. For example, if there are 12 total coins and the final result is that 9 are sorted correctly, 2 incorrectly, and 1 gets stuck in the machine, the final score would be:
$$\text{accuracy}=100\%\left(\frac{\text{9}–\text{2}–\text{1}}{\text{12}}\right)=50\%$$

For the prototype round, grades were calculated as follows:
$$\text{performance grade}=50\%\left(1+\frac{\text{[your accuracy]}–\text{[lowest accuracy]}}{\text{[best accuracy]}–\text{[lowest accuracy]}}\right)$$
$$\text{cost grade}=50\%\left(2–\frac{\text{[your cost]}–\text{[lowest cost]}}{\text{[highest cost]}–\text{[lowest cost]}}\right)$$

Based on the results of the prototype testing, the following scoring system was determined for the final round:
$$\text{performance score}=100\%\left(1–0.65\text{exp}\left(–\frac{\text{[your accuracy]}}{\text{0.2}}\right)\right)$$
$$\text{cost score}=50\%\left(1–\text{erf}\left(\frac{\text{[your cost]-\$35}}{\sqrt{\text{2}{\left(\text{\$13}\right)}^2}}\right)\right)$$