What is the greatest power of two that is a factor of:
19!
130!
Can you do both of the above mentally i.e w/o pencil/paper, computer etc?
- via Sid Hollander

## Monthly Archives for September, 2013

## Another detective puzzle

Sherlock Holmes walks into a room and finds a man dead with a bullet hole through his head. There's a gun on the floor. He hits play on a tape-recorder nearby and it reads: "Dear God. Forgive my sins. I now offer you my soul." followed by a gun shot.
Sherlock Holmes concludes that it was murder and not suicide. Why?
- Via Best Brain …

**Continue reading the story**"Another detective puzzle"## Detective puzzle

There are five people. One of them shot and killed one of the other five. Which man is the murderer?
1. Dan ran in the NY City marathon yesterday with one of the innocent men.
2. Mike considered being a farmer before he moved to the city.
3. Jeff is a topnotch computer consultant and wants to install Ben's new computer next week.
4. The murderer had his …

**Continue reading the story**"Detective puzzle"## Sorting hats

There are 16 hats: 4 red, 4 blue, 4 green, 4 yellow. Each of the 4 hats of a color are to be labeled a '+','-','x' or '÷' and all 4 arithmetic sign labels must be used exactly once per color. Thus a hat can be identified uniquely by it's color and symbol. Arrange the 16 hats in a 4x4 grid so that no two …

**Continue reading the story**"Sorting hats"## consecutive hats

There are 30 hats in a row. 15 of them are red and the remaining are blue. Show that there are 10 consecutive hats consisting of 5 red and 5 blue hats.
via AMS puzzle corner

## Maximum possible subsets

Suppose you have 100 integers whose sum is 1. What is the maximum number of subsets whose sum is positive?
via AMS puzzle corner 14

## Knapsack problem

Suppose you have goods numbered 1,2,3....n that you want to transport. Good i has value V_i and weight W_i. You want to transport as much value as possible over an airplane. However, you are allowed to transfer a maximum weight of W. You wish to maximize the total value of goods transported subject to the constraint that the total weight is at most W. Assume …

**Continue reading the story**"Knapsack problem"## Lock that can close without a key

There are locks that needs a key to open, but can be closed without using the key.
Imagine the following scenario: You are the only person in the home who owns the key to the shed. A week ago, you open the shed, store some stuff inside, check whether everything is in order, then exit the shed and finally lock it. Later the police come …

**Continue reading the story**"Lock that can close without a key"## Winning at roullete

Suppose you have unlimited time and cash. Can you guarantee that you will win in the roulette?
via Stack Exchange

## Perfect square

Let x,y be chosen independently and uniformly at random from {1,2,...n}. Let be the probability that (x+y) is a perfect square. Find
via UC Davis