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.
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.
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.
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.
- I don’t get this?
- What don’t you get?
- John and Paul are both on the committee and they sat next to each other!
- Please explain!
- A committee of three was selected at our last meeting. There were 20 people sitting around the round table and three people were selected randomly.
- And your point is?
- Isn’t it incredible that two of the three elected sat next to each other?
- Do you expect the election was rigged?
- I don’t know. I just want to know what the chances are that at least two of the three committee members sat next to each other.
Problem source: Fortnight problem, Department of Computer Science, San Diego State University.
Problem source: Strategies for solving problems in the BAMO contest (the Bay Area Mathematical Olympiad) by Tom Davis.
A big circle is painted in the corner of a room. It touches the two walls. If you were to paint a small circle that touches the big circle and the two walls, how big would it be?
Problem source: dansmath.
- I am no big typist. As a matter of fact, when I typed my last novel I didn’t look up from the keyboard even once! I was too busy making sure the fingers hit the right key. Big was my surprise when I discovered that the text was all gibberish.
- You are no big novelist either, if I may be a bit honest.
- OK. But this was worse. I discovered that every time I hit a key I got what seemed to be another key selected randomly.
- Let’s see if I understand. When you hit ‘a’ did you get the same letter every time?
- Yes, that is correct.
- Interesting.
- I got every character as before, but by pressing a key I was not used to. Actually, some of the keys gave the character printed on them, but most did not.
- So what did you do?
- I typed it again, but this time I typed what I had printed out from my first attempt.
- Did that help?
- No, I can’t say it did.
- So why on earth did you do it?
- I have an intuitive feeling that if I continue to type in what I print out sooner or later my novel as intended will appear!
- Quite a feeling!
- Thank you?
- How many keys do you have on your keyboard?
- 46 or n, I can’t remember.
- If you are right, I wonder how many times you would have to retype your novel.
Problem creator: Leonid Broukhis. Source: wu:riddles.
Source: Division by Zero.
How many four digit numbers are there where the digits are ascending from left to right?