## The more you take away

The more you take away, the bigger I become. What am I?

Hole.

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The more you take away, the bigger I become. What am I?

Hole.

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What is a tree's favorite drink?

Root beer.

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Why is it against the law for a man living in Delhi to be buried in Mumbai?

Because he is still living.

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Two baseball teams played a game. One team won but no man touched base. How could that be?

They were all girl teams.

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What has 4 wheels and flies?

A garbage truck.

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A man takes a barrel that weighs 20 pounds and puts something in it. It now weighs less than 20 pounds. What did he put in the barrel?

He put a hole in the barrel to make it weigh less.

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A lemon and an orange were on a high diving board. The orange jumped off. Why didn’t the lemon?

Because it was yellow.

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What always comes into a house through the keyhole?

A key.

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There are n coins in a line. (Assume n is even). Two players take turns to take a coin from one of the ends of the line until there are no more coins left. The player with the larger amount of money wins.
Would you rather go first or second? Does it matter?
Assume that you go first, describe an algorithm to compute the maximum amount of money you can win.
Note that the strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.
Example 18 20 15 30 10 14
First Player picks 18, now row of coins is
20 15 30 10 14
Second player picks 20, now row of coins is
15 30 10 14
First Player picks 15, now row of coins is
30 10 14
Second player picks 30, now row of coins is
10 14
First Player picks 14, now row of coins is
10
Second player picks 10, game over.
The total value collected by second player is more (20 + 30 + 10) compared to first player (18 + 15 + 14). So the second player wins.

Going first will guarantee that you will not lose. By following the strategy below, you will always win the game (or get a possible tie).
(1) Count the sum of all coins that are odd-numbered. (Call this X)
(2) Count the sum of all coins that are even-numbered. (Call this Y)
(3) If X > Y, take the left-most coin first. Choose all odd-numbered coins in subsequent moves.
(4) If X < Y, take the right-most coin first. Choose all even-numbered coins in subsequent moves.
(5) If X == Y, you will guarantee to get a tie if you stick with taking only even-numbered/odd-numbered coins.
You might be wondering how you can always choose odd-numbered/even-numbered coins. Let me illustrate this using an example where you have 6 coins:
Example
18 20 15 30 10 14
Sum of odd coins = 18 + 15 + 10 = 43
Sum of even coins = 20 + 30 + 14 = 64.
Since the sum of even coins is more, the first player decides to collect all even coins. He first picks 14, now the other player can only pick a coin (10 or 18). Whichever is picked the other player, the first player again gets an opportunity to pick an even coin and block all even coins.

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What did the schizophrenic bookkeeper say?

I hear invoices!

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