5, 25, 325, 4325, ?
via Dan Hersham

## Monthly Archives for September, 2013

## Coloring planes

Every point in the plane is colored either red or blue. For a given distance d, show that there always exist 2 points that are distance d apart whose end-points have the same color.
via cut the knot

## Clubs

A town has n people and m clubs. Each club has an odd number of people. Each set of 2 clubs has an even number of common members (can be 0 too). Show that m cannot be greater than n.
via Math Exchange

## A game of probabilities

A standard deck of 52 playing cards is shuffled. Then the cards are dealt one at a time from the top of the deck until an ace occurs. Then the next card is handed over to you.
What are you more likely to obtain? The ace of spades or the two of hearts?
- via Math Exchange

## Look at each other

A group of n people are asked to stand against the wall. Each person chooses a location uniformly at random on the wall and independent of the other people. Then each person is asked to look at his nearest neighbor from the group. What is the expected fraction of people (as a function of n) who are looking at each other?
via Math Exchange

## Reflecting beads

Four identical beads are at the corner of a square on a flat table of infinite dimensions (a plane). Any bead can move by reflecting itself with respect to any other bead, i.e. A bead can move from position x to position y if there is a bead at position (x+y)/2. Is there a sequence of moves that can reposition the four beads to the …

**Continue reading the story**"Reflecting beads"## Removing apples

Alice and Bob take turns to remove apples. Alice must remove at least a0 apples and no more than a1 apples in his turn unless there are less than a0 apples in which case Alice removes all the remaining apples. Bob must remove at least b0 apples and no more than b1 apples unless there are less than b0 apples in which case Bob removes …

**Continue reading the story**"Removing apples"## How much is Jennifer?

Susan=10
Arabella=20
Jim=5
Neil=5
Richard=10
Jennifer=?
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via youtube

## A geometry puzzle

Let ABCD be a square of side 1 unit. Let E,F,G,H be the mid-points of AB,BC,CD,DA respectively. The lines FA, AG, GB, BH, HC, CE, ED and DF enclose a regular octagon of side s. Express s^2 as a rational number.
via Quora.
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Solution can be found here