Challenge Problems To Try

Presented by Cory M. Wisnia, A MendoWorld Science Tech Guy
cwisnia@mcn.org
Mendocino Middle & High School, Mendocino CA 95460

http://www.mcn.org/ed/cur/cw/cwhome.html

1.[Challenge Problem 1: Building A Fence](...very open-ended!)
2.[Challenge Problem 2: Tiling A Bathroom](...more structured)
3.[Challenge Problems 3: Jeannie's Car Loan](...fairly structured)
4.[Challenge Problems 4: The Cookie Game](...fairly structured)

1. Building A Fence

It turns out that the Wizard has an RV Park and Campground up in the Sierras (this is actually true!). He wished to replace an old fence along one side of the perimeter of the park with a newer, more eye-appealing one. The ground was somewhat uneven, rising 4 feet over the first 125 feet, and then dropping one foot over the last 75 feet. Your task is to coast out a new fence for the Wizard, using actually costs for real materials found at your local lumber/hardware store.

If you accept this challenge, you will need to do a picture or model of your design, and then scan it into a pic file and send it plus your budget to this e-mail address (cwisnia@mcn.org) or send it via snail mail to: Fence Challenge Problem #1, POB 421 Mendocino CA 95460. The best projects will demand a 3-d model (1 cm = 1 foot scale), but the detailed budget, including material costs and potential labor costs, (don't forget a gas-powered posthole digger!) plus an explanation of your design, is essential.

To start, you might think about the kinds of elements an excellent presentation/solution of this problem might include. Create a simple checklist to make sure you include as many of those elements as possible. The Wizard will try to post as many interesting pictures of solutions, plus budgets as possible. And your name and school will be listed in the credits. You can send GIF files on disc if you don't wish to send models. Send only text by e-mail since crossing platforms is usally a problem with attachments.

The only real criteria for your fence is that it needs to be at least four feet above the ground, and that it needs to be sturdy enough to withstand snow loading during the winter. The old fence fell down every winter! If it isn't painted, it may need some kind of staining or water-sealing. It needs to be 200 feet long and must rise and fall as written about above.

There are pictures available of the ACTUAL fence as built by the Wizard this August (1996) here at the page, plus the one replaced, but it should be understood that the way the Wizard built it is only one of many possibilities. You shouldn't feel the need to copy that fence. It was building this fence, which took him about 1.5 months, which gave him the idea for this problem.

If you would like to see a series of pictures of the fence that the Wizard built, plus one which shows part the original fence, click on the thumbnail shown here. The Wizard's RV Park and Campground is up in the Sierras at Graeagle CA (4500 feet on the Upper Feather River in Plumas County!

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2. Challenge Problem 2: Tiling a Bathroom Floor

The Wizard is remodeling his house (again, a true story!). He has finished the bathroom except for the floor. Here is a FLOOR PLAN of his bathroom (not perfectly to scale, BTW, but with some possibly useful measurements):

The shaded part is what needs to be tiled, including around the base of the sink and tiolet.

When he visits The Tile Shoppe in Fort Bragg, he sees several interesting ceramic tiles, which come in three sizes and different prices.

Question: How Many Of Which Tile Type Should The Wizard Buy?

Can you be a tile buyer for the Wizard?! Here are the tile sizes and prices (add sales tax of 7.25% to all values):

The more tiles needed, the more work, and more grout will also be needed, so add an extra $.50 per tile for the 8" square tiles to balance out the extra time and materials it will take to use those.

1)....Using the floor plan and the measurements listed, which tiles and how many should he order?

2)....You need to order 10% more than needed because ordering just a few extra will not be easy. But since returning tiles is also not allowed, you don't want to order too many.

3)....Can you estimate how many of each tile the Wizard should buy if he decides to go with any of the possibilities. If the price is close, he may decide to go one way or the other depending on the stype or pattern.

NOTE: Tiles may be cut diagonally, or parallel, but complicated shapes aren't possible with the tile cutter he is renting.

There is also one larger tile on sale. While he really isn't as excited about the color, the price seems pretty good:

Eternity (On Sale)---12" square: $2.50 per tile

How much could he save by getting this type of tile?

Other Possible Issues

Which is the best direction to lay out these square tiles? (Parallel to the tub and shower or to the walls?)

Approximately how many tiles will need to be cut? (Can you use the cut off sides frugally?) How much money will just buying the tiles cost, if you went with one of the first three listed (excluding the sale tile). The wizard would like to spend under $160. Is this at all reasonable?

The Wizard would be happy to post your solution(s) to these two problems listed above. In fact he may wait to buy the tile until after he receives a couple of good solutions, so please write!! For your solution, some things that might be included are: a GIF file which shows how the floor looks, with all the tiles drawn in. While it is important that space for grouting be left (about 1/8"), this is more of an estimate that an exact plan. So you don't really have to figure that in unless you want to. Show how much each of the possibilities will cost if possible.

If you like, take a look at your own bathrrom, draw a picture and make a GIF file, and challenge us to figure how to tile YOUR bathroom using the prices and tiles listed! If you do that, include your own estimates of a solution. Another thing to do for further consideration: since the Wizard lives in an out-of-the-way place, perhaps you can get a much better deal, even on high-quality ceramic tiles if you are near a city. How much do tiles like these cost in your area. Is it worth the Wizard's time to drive 100 miles to Santa Rosa to the nearest ColorTile store?

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3. Jeannie Wants To Buy A Car!

Click --here-- to go to two compound interest challenges involving buying a car.

Jeannie wishes to buy a car and has limited resources. The first problem has her figuring out how interest rates are used when purchasing a car, and the second gives a more realistic scenario that each of us faces when we try to buy a new or used car, involving limited resources, several interest rates and several time periods. These problem were loaded on-line on March 7, 1997, and were given as enrichment problems to an Algebra II class which was studying compound interest rates! Send your answers to the Wizard and he'll publish or evaluate them with credit given!

4. The Cookie Game

This is the NEWEST problem! It involves working with Growth and decay curves, and came out of first working with the IMP unit "All About Alice", then applying those concepts to an Algebra II class, so it is pretty advanced. But it also can be fun if you really try it. If you are a teacher or student and come up with a better equation to play this game, which is related to PIG, and send it in to me I'll post YOUR equation with full credit given to you! Click --here-- to go to rules about how to play this game. Pre-requisites: you'll probably need to know something about growth and decay curves or equations of the type: y = ab^x or y = A(1+ r)^x. Good luck!

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