Friday, December 23, 2011

Run buddy, run.

My husband has encountered this real-life puzzle last week and we are both looking forward to hearing your suggestions.

He wants to organize a running race at his work. His center consists of different groups. The group that will win the race will be awarded with a significant prize. We need your help defining the winner.

What does it mean for a group to win the race? Here are your guidelines:
  • Groups can be of different size, but each group should have equal chances to win.
  • Wide participation should be encouraged (and rewarded) more than running performance. 
  • Running performance should also be taken into account.
  • The runners that finish first, second and third should add special bonuses to their groups' total result count.

Therefore, in order to rank each group in this race we need some kind of a function that takes into account all of the above requirements, uses participation and run results and produces a number for each group. Group with the largest number would be declared the winner.

Top image by JerryFest, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday December 25th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.


anne-marie said...

To encourage wide participation and the feeling of being part of a team and rewarded, I think of a kind of a relay race.
The people with no difficulties to run long distance could be placed at the begining of the race and the other runners of the team along the path depending of their ability of endurance, their health..
The first person or persons have to pass a stick or something symbolic to the other person or persons of their team and so on.
However, the first person or persons of the same team, instead of stopping after the first relay could continue running and finishing the race but should not help with the stick except if a person cannot do his/ her part to pass the stick for a reason or another.
If the group is large enough, they can organize themselves in such a way that at least twogood runners

anne-marie said...

I continue here..
In such a way that at least two good runners are going first lbecause after the relay, one could continue the race and the other one can make sure that the stick is passed..
Well, you have the idea, everybody can participate, there is strategy, team work and it is rewarded and it is also a race...the first people can continue the race so the team with the largest amount of people is rewarded and the stick should also be at the final line because it is a team work.

anne-marie said...

Merry Christmas everybody!

anne-marie said...

Ok, I did not answer the question :)
This my idea.
Give a weight to each variable: participation, running performance..
For example, if the maximum weight is 1 and a weight of 0.6 is given for the partIcipation x, we have 0.6 x.
Now if the group consist of 15 people and 13 come then x=13/15.
It has to be done with each variable and at the end, all weight * variable are added. The team having a bigger score win.
Sorry for that!

Jerome said...

We could broaden the base. Depending on how many oc these I can think of perhaps you could have

The office Iron Person Triathalon
1. Running
Choice A Brutal
first 30
Second 20
Third 10
Participation: 5

Total for team = total divided by number on team
Weight: 60

Event B
Speed typing: Type :
The quick brown fox jumped over the very lazy dog.

I put in the extra word just to make mistakes.

First 30
Second 20
Third 10
Participation 5

Team Score: Team Total divided by number
Weight: 20 (More if you all use computers).

Golf Shot:
I know it's winter where you are. You can get colored golf balls.

You can determine the clubs used by a person's handicap or you can use those golf balls that are practice balls. If you really relish goofy, you can use a tennis racket. He who hits the furthest wins. You could also divide groups by gender -- or is that sexist.

Scoring Males/Females each team is scored as follows.
F 30
S 20
T 10
P 5

Team Score: Team Total divided by particpants.
Weight: 20 Less if the typing thing is more.

Office Pentathalon
Event Four
How about something with a Frisby?
Pitch the furthest or pitch the most accurate. I'd pick the frisby if I were you. People who play frisby golf have an advantage that others do no. These things are specially made for accuracy or distance.

F 30
S 20
T 10
P 5
Bonus 2 if people have dogs that can catch a Frisby at least 30 paces away. 3 points if the dog can catch the frisby from a running start by his master's heal.

weights have to be readjusted for 5 events.

Total Team Scores: Total + Bonuses divided by the number of participants.

Event Five
I'll leave this open to everyone's imagination. There must be something office related that you can make into a game.

Merry Christmas

Ilya said...

Let's rank every group in terms of average time. To calculate the average time of a group:
* 1st, 2nd and 3rd places count as 85%, 90% and 95% of their actual measured time - this accounts for the top 3 bonus.
* everyone else gets their actual time added in
* people from the "group" who did not run get added as 200% of the last measured time
* once every group's total time is calculated, the average is obtained by dividing by the size of the group.

Here is an example of what a race might look like between groups 1 and 2

A: finished 1st in 10 min (gets added as 510 sec)
B: finished in 15 min (gets added as is)
C: did not run (gets added as 40 min)

Group 2:
D: finished 2nd in 11 min (gets added as 594 sec)
E: finished 3rd in 12 min (gets added as 684 sec)
F: finished last in 20 min
G: did not run (gets added as 40 min)

Group1 average is 1270 sec, Group2 average is 1219.5 sec, so Group2 wins, their higher participation rate (3 out of 4) giving them a boost.

Maria said...

Very interesting suggestions. I will pass it on to my husband.
Anne-marie - I love your relay idea. It is more fun than a regular race, it counts performance and participation. However, a group that sends only one fast runner will win over a group of 10 where everyone participates but haven't practiced for a while. You are right - we have a weighted sum.
Perhaps something like: w1 x participation ratio + w2 x running performance and possibly + w3 x first three places bonus, where each variable is normalized to be between 0 and 1.
However my father thinks that instead of "+" everywhere there should be "x".

Participation ratio is easy: number of group runners / total number of people in the group.
Running performance is more tricky: perhaps add 1 for each slow runner, 2 for medium speed, 3 for fastest. Divide all by the # of group runners x 3.
First places bonus: say 1 for 1st place, 0.8 for second, 0.6 for third.

Jerome - your typing contest, Frisbee and golf competitions are perfect for a holiday party and surely make anyone who is not keen on running feel part of the team.

Your scoring idea for each competition is very original:
First 30
Second 20
Third 10
Participation 5

Total for team = total divided by number of the people on team

This way you encourage performance and participation simultaneously. However there is still too much weight for the first three performers. Take two 10 person teams:
in the 1st team, only 3 people participate and take 1st, 2nd and 3rd places = 60 points. Divide this by #of people on the team 60/10=6
In the second team everyone participates but no one wins 5 x 10= 50 divide by #of people on the team 50/10=5 First team wins but remember - we wanted to encourage participation more than performance. Perhaps the weights should be adjusted.

Ilya - I think your solution may be the simplest and closest to the goal. I specially like the idea of adding 200% of the slowest time for each non-runner. A bit cruel but definitely encourages participation.

Feel free to post your comments and more suggestions below. Enjoy the holiday week!
For now - a puzzle point for anne-marie, Jerome and Ilya.
I guess daily jogging should be one of my New Year's resolutions.

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