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I shamelessly stole this puzzle from another website

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I stole this puzzle from another website, I liked it and thought the people that typically read this blog would like it too. Here it is:


A friend of mine has £100 in a bank account.  Whenever he takes out money he records how much he has taken out and the balance.  Here are his accounts for last week….
Withdrawn Balance
40 60
30 30
20 10
9 1
1 0


There is one small problem – the WITHDRAWN column adds up to 100, but the BALANCE column adds up to 101 – how can this be the case?

Comments

Gravatar Image1 - Well, as usual, it's a trick question. The balance isn't supposed to add up to $100. Why should it?

Gravatar Image2 - There's no expectation at all that the sums of the two columns should match. The numbers were chosen in such a way that they would almost match, but that's just to fool you. If the withdrawals had been in even increments of 20, the balances would have been 80, 60, 40, 20, and zero, which add up to 200.

Now for the complete geekery...

Let the left column be represented by a + b + c + d + e = 100

The right column is (100-a)+(100-(a+b))+(100-(a+b+c))+(100-(a+b+c+d))+(100-(a+b+c+d+e))

The last term of the that expression is zero, so the right column simplifies to (100-a)+(100-(a+b))+(100-(a+b+c))+(100-(a+b+c+d))

That rearranges to 400-4a-3b-2c-d

Notice that at this point everything is completely independent of the actual values of a, b, c, d and e. You can pick any values, as long as they sum to less than 100. So pick 1, 1, 1, 1 and 96. In that case, the right column comes would sum up to 390. That's the maximum value you could find there.


Gravatar Image3 - Last paragraph, meant to say as long as they sum to exactly 100.

Gravatar Image4 - This is my favorite number puzzle.
Similar but harder to figure out. Emoticon


Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

Gravatar Image5 - Yeah same kind of thing Hynek. Still confuses people Emoticon

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