Math Quiz

Sunday was the MCM. They awarded over 20,000 medals.
Can chess tournaments learn any thing from the Marine Corps Marathon?
http://www.washingtonpost.com/wp-dyn/content/article/2007/10/28/AR2007102801507.html

Umm…how about: “They know how to run stuff.”

Ah, I can’t resist a pun?!

Tim

Don’t forget the warnings that it’s an ESTIMATE.

In the real world, I think you can depend on it - but in THEORY you might get busted. Have a back-up plan.

I just tested Ken’s formula against a few actual scholastic tournaments across 20 sections. In 14 of them the formula predicted as many or more players with a certain target score than actually acheived that score. There didn’t seem to be any pattern as to how far it was off vs. the number predicted, the number of rounds or the number of entrants, but it would have served the purpose of making sure enough trophies were on hand.

In 6 of the sections, which all happened to have 6 rounds (but 2 of the sections above did too) it under predicted by 1 to 4 players, but there doesn’t appear to be any consistent % that it’s off. Adding 5% of entrants would have covered 5 of the six.

Although my sample size is small, it looks like the formula works well for up to 5 rounds, then I’d need to add a little buffer for any more rounds above that.

Again, thanks for the help!

Grant Neilley

  1. What’s green and very very far away?

Would that be a lime at infinity?

Also, in my experience, kids learn RealFast that “participation” awards are “loser awards”.

We give medals (or similar items) to every player, even those who also win trophies. So far it seems to be going over well, except that I have piled up quite a collection of extra medals that never got used. (I know we can re-plate them for future use, but we haven’t given out the same kind twice yet.)

I like the idea of a chess set, but is there perhaps something even more practical for young kids to take home? I’m considering maybe using small booklets of tactics positions as the “participation” prizes instead. They could have a nice, fancy cover for the event and would be more valuable to many players (I think).

The booklets are an interesting idea, Mike, any idea what they might cost to produce?

In our last scholastic, we had drawings for a variety of door prizes throughout the tournament. Each person drawn could take their choice of items available. The sets and clocks were first to go, not surprisingly. Small magnetic sets were also very popular, and aren’t too expensive. The books were the last things to go, so even though I think they were some of the most useful/helpful items, those weren’t the things the kids valued most.

Grant Neilley

Umm…how about: Tim Just

Indeed they do. It is the largest marathon in world that does not offer prize money. All you get is a shirt when you enter and a medal when you complete 26.2 miles. It is all about participation. The bands and the 150,000 cheering supporters along the route make it a great event.

The booklets are an interesting idea, Mike, any idea what they might cost to produce?

It obviously depends on the quantity produced (larger amounts get slightly better rates) but we’re about to produce about 1100 copies of a 36 page booklet (8.5x11 folded over, with a cover too) of tactics exercises for $1000. So they could easily be produced and distributed for between $1 and $2 each.

Of course, the real trick is to have several different ones so you’re not giving kids (or adults!) the same one twice.

We’ve also given a bit of thought to t-shirts, though these would obviously be a bit more expensive.

T-shirts have two advantages that may outweight or factor into cost considerations:

  1. They WILL get worn, especially if they have great graphics.

  2. You can sell ad space on t-shirts.

  1. My son wears some of the old t-shirts that organizers gave me for directing, and I still where a sweatshirt from the 1994 K-8 state championship (it is a little tighter than it used to be, maybe I’ll pretend that it has shrunk).

  2. You may also be able to sell ad space in tournament booklets. For one of the IL K-8 state championships (1985? in Peoria) the organizer (Lou Betts) said that he did such a good job in selling ads in his tournament book that all of the expenses would be paid even if nobody showed up to enter and play.

Marathons and other endurance events tend to give finishers medals or tee shirts to everyone who completes the event. When doing a marathon, I’ve never considered these items as a loser’s prize. On the other hand it’s not having or not having a finisher’s medal that makes me decide whether I’ll do the event or not. The possible exception might be the Nike Women’s Marathon that I did two weeks ago, where the “finishers medal” is sterling silver Tiffany necklace.

brightroom.com/view_user_pho … s&BIB=8602

At the scholastic nationals a well designed teeshirt tends to sell out on the first day. (In the most popular sizes.) Running races and triathlons tend to give each participant a tee shirt. The back is covered with all the race sponsor names and logos. Giving away a shirt doesn’t seem to cut in on the sales of other race logoed shirts.

Another item that has become a popular give away is the nylon drawstring backpack. They’re inexpensive, and easy to silkscreen the event logo on to.

Correct. Actually, the lime at infinity. (There’s only one line at infinity. There are infinitely many points at infinity.)

Bill Smythe

does the line at infinity interpolate all of the points at infinity?

discuss.

All the points at infinity are on the line at infinity, if that’s what you mean. (I’m guessing, though, that you are once again being clever, and over my head.)

For those who are under even my head, the points at infinity and the line at infinity are added to the ordinary Euclidean plane in order to convert it to a projective plane.

Specifically, the Euclidean plane can be thought of as the beast whose points are ordered pairs (x,y) of real numbers, and whose lines are equations of the form y=mx+b or x=c, where m,b,c are real numbers. A point is on a line in case the coordinates of the point satisfy the equation which is the line.

Now define a “point at infinity” to be an equivalence class of parallel lines, and define a point at infinity to be on a line in case the line is in the equivalence class.

Also postulate the existence of a “line at infinity”, and define a point to be on the line at infinity in case the point is a point at infinity.

Now you have a true projective plane, where for every pair of distinct lines, there is exactly one point which is on both lines. (No more parallel lines.)

Bill Smythe

This is a really old thread, but I didn’t see an actual answer to the OP.

What is the maximum number of trophies (or other prizes) that would be needed to cover an event?

n = number of players
r = number of rounds
s = score required to get a prize

Then the maximum number of prizes is calculated by:
b/s[/b]

So for a 4 round tournament with 10 players and a cutoff score of 2.5, you proceed as follows:

ceiling(n/2) = 5
(5 points available per round. If there is an odd player, then a single full point bye is added, hence the ceiling function)

ceiling(n/2)*r = 5*4 = 20
(20 total points available in the tournament)

20/2.5 = 8 which means you can have at most 8 players win a trophy.

This only works if a single full point bye is allowed per round (i.e. if there are multiple sections, you need to perform this calculation for each section)

I think the answer was that there is no universal answer to the question.

Since most of you are simply looking for an upper bound, why not just say that the maximum number of prizes is n?

Bill Smythe