think again!

The object of this game is to collect as many gems in your mancala (the large cup on the right) as possible. You and the computer take turns moving the gems.

Play it here.

The game was found on this page, which is full of math games.

If the front of the cathedral has the shape of an isosceles triangle and the base is 5/6 of the height and the perimeter is 55m and the temperature is freezing how tall is the church?

Problem source: Mattenøtt, NRK.

If you’re robbing a bank and you’re pants fall down, I think it’s okay to laugh and to let the hostages laugh too, because, come on, life is funny. - Jack Handy

Three kids share 770 peanuts. Every time Alan gets 4 peanuts, Boris gets 3 peanuts, and every time Alan gets 6 peanuts, Carla gets 7 peanuts.

How many peanuts does Alan get?

Problem source: Mattenøtter, Teknisk Ukeblad.

Black holes result from God dividing the universe by zero.  - Unknown

I’d like to ask the Think Again crowd for help with a real world problem.  It involves tree sap, specific gravity, a siphon, a hot flame, and maple syrup.  I want to know if my suggested contraption will maintain a consistent water level.

I am trying to make maple syrup.  Here’s some background information on how the process works.  This time of year, tree roots are sending sugar water to the branches.  The branches aren’t ready, so the sugar water goes back down to the roots.  I drill a hole in the tree and place a tap in that hole.  The tree say drips out of that hole into my bucket.

That bucket accumulates the tree sap which is about 97.5% water and 2.5% delicious maple syrup.  I would like to eliminate the water by boiling the sap.  I would like to boil it in a flat pan on a gas grill.  Somehow, though I need to keep adding tree sap as water boils off.  It is bad to overcook the syrup.

That’s where the siphon comes in.  I will have the sap in a 5 gallon (about 18 liter) jug.  I would like to place that jug in a garbage pan filled with water.  Finally, I would like to run a sap filled siphon from the floating jug into evaporation pan.  The garbage can would be sufficiently large, and the fluid levels would start out equal.

My thought is that as water boils off, more sap will siphon from the jug.  As sap leaves the jug, it will rise in the garbage can.  I am hoping that, once equalized, the water level with respect to the ground will stay the same in both the pan until the jug is empty.

So here’s my question: will it work?  How important are the specific gravities of the water and the sap?  Assuming the jug rest on the side of the garbage can, does the shape of the can matter?  Does the weight or density of the jug matter?  Does the weight or density of the siphon matter?  Does anyone have a gently used waffle iron?

In advance, I thank you.

Email from Alan M Robertson yesterday.

Remember that you too can send problems to be posted on the blog. Real or imaginary.

Obvious is the most dangerous word in mathematics. - Eric Temple Bell

A sultan decides to check how wise his two wise men are. The sultan chooses a cell on a chessboard and shows it to the first wise man. In addition, each cell on the chessboard either contains a rock or is empty. The first wise man has to decide whether to remove one rock or to add one rock to an empty cell. Next, the second wise man must look at the board and guess which cell was chosen by the sultan. The two wise men are permitted to agree on the strategy beforehand. What strategy can they find to ensure that the second wise man will always guess the chosen cell?

Problem source:  Leonid Makar-Limanov via Tanya Khovanova’s Math Blog.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.  - John von Neumann

ABCD is a square. Where must the ball hit CD to end up, sooner or later, in A. In the drawing it hits CD 2/3 from D to C and ends up in D.

Problem source: mathschallenge.net.