Today, I share a few of my favoirtes, and invite you to share yours.
1. I will supply answers in tomorrow's diary
2. If YOU want to supply an answer, or ask about one, go ahead, but PLEASE put it in your title so that people who don't want to see don't do so by accident.
3. I encourage people to submit their own favorites. But PLEASE give it a name, and indicate if any advanced math is neeeded, and whether it has a known solution
OK - enough. On to the puzzles
Puzzle 1 - Two coins - No advanced math. Known solution.
You have two ordinary US coins in your hand. The total value is 30 cents. One of the coins is not a quarter. What are the two coins?
Puzzle 2 - Counterfeit coins. No advanced math. Known solution. You have 5 bags of 200 coins each. One of them contains counterfeit coins. The others contain real ones. Counterfeit coins each weigh 90 grams. Real coins each weigh 100 grams. You have a scale (a regular scale that give a weight, not a balance), assume it is very accurate. Using the scale only once, how can you tell which bag has the counterfeit coins?
Puzzle 3 - More counterfeit coins. No advanced math. Known solution. Same as puzzle 2, except now you don't know how many bags have counterfeit coins. How many times do you have to use the scale?
Puzzle 4 - Chicken and egg. 5th or 6th grade math. Known solution. If a hen and a half can lay an egg and a half in a day and a half, how many eggs can one hen lay in one day?
Puzzle 5 - Letters. No advanced math. Known solution.
What comes next in this sequence?
Puzzle 6 - xyz. At least algebra, maybe more. Might have a solution, I don't know.
Either solve this, or prove it can't be solved:
x + y + z = 1
x^2 + y^2 + z^2 = 2
x^3 + y^3 + z^3 = 3
Puzzle 7 3n + 1. Maybe advanced math. No known solution.
Take any positive integer (counting number). If it's odd, multiply by 3 and add 1. If it's even, divide by 2. Repeat until you get to a loop.. For example, if you start with 7 the sequence is
7 - odd - 3N + 1 = 22
22 - even - half = 11
11 - odd - 3n+1 = 34
34 even half = 17
52 26 13 40 20 10 5 16 8 4 2 1
it's been tested for a LOT of numbers (into the billions) but it hasn't been shown to ALWAYS work, and I don't think they know much about how long a number takes to get to 1
And add yours!