I was at first. The only explanation I can think of is that each of the 4 different pieces becomes 1-2% bigger as they move around so that when then form a rectangle there is enough space for an extra block.
Scratch my 1st theory. Here is the actual answer. The 1st shape (square) is not really a square. It looks like one to the naked eye but if you stick a ruler or some other measuring device you will notice that all sides are not equal. My conclusion: It was never 8*8 = 64 turning into 5 *13 = 65 It WAS 8 * 8.125 = 65 turning into 5 * 13 = 65 If anyone has a better explanation please let me know..... I know I had too much time on my hands.
bigballer -- you're right, none of the squares at the edges (where the pieces have been spliced) are correct squares.
It's like the story where three guys go into a motel. The clerk says its $30 to stay. They each pay $10. The clerk realized he made a mistake on their total by $5. Tells the bell boy to bring their change up. Bell boy decides that he's going to only give the guys back a dollar a piece, so he gets two dollars. Bellboy gives them all back a dollar. Bellboy keeps the two dollars. Each guy now has $9. Bellboy has $2. =$29. What happened to the other dollar? I love this problem!
I think you meant to say, "Each guy has now paid $9.", which is the kicker to the problem. Anyways, this is faulty logic, which is why the problem is silly. The way you determine how much money each person paid is to figure out the total sum of money invested in the hotel room, which is $25. The additional $5 is to be returned amongst each person. To start off, each person paid $10 each. Now, the hotel clerk has $30 cash in hand. The hotel clerk gives $5 to the bellboy, who takes it to the hotel room. Now: Clerk = $25, Bellboy = $5, 3 Guys = $0. Bellboy goes up to room, gives each guy $1. Now: Clerk = $25, Bellboy = $2, 3 Guys = $3. The way the problem tricks you is by saying each guy paid $9 for the room. This is not true, each guy paid ($25/3) = $8.33 for the hotel room. The catch is that the problem fails to account for the fact that the guests also contributed $0.67 each for the unintended 'tip' for the sneaky bellhop. Therefore, the problem is not of a missing dollar, only fuzzy math.
I was just thinking about the hotel problem the other day... I couldn't remember how it went. I only remember the way to solve it was completely different than how the problem was stated.
Any personwho thinks math is absolute, consider this.... Why can't you do something as simple as divide 10 by 3?
Here's another famous statistics problem: You're on the game show Let's Make a Deal and you’re given a choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, Monty Hall, who knows what’s behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to stay with door No. 1 or switch to door No. 2?’ Should you stay with door No. 1, or should you switch?
Shiiiiiiit. You take the goats, and go home. Them's some good lovin'. Seriously, I've seen this before. Just because he's shown you one of the bad doors doesn't eliminate any of the statistics. It affects your emotion. Are they going to screw me again and have two bad doors, or do they have two prizes, in which case I could get a bigger prize. If you "knew" only one door had a prize, it helps you figure it out better in your head.
Hmm. If one door has a car and the others have goats, that means that there's 2 goats. So if you know that door number 3 is a goat, that means that you have a 50/50 shot at the car. It's still a guess on which is the right one. So it doesn't really matter if you switch or not. Although you'll be absolutely filled with self-loathing hate if you choose the wrong one: If you switch because you had the right one all the time, and if you don't switch because it's as if the host warned you about it.
THe key is that Monty knows where the car is. So the one door that's eliminated was not random. Essentially, you had a 1/3 chance of being right originally and a 2/3 chance of being wrong. By giving you the choice of one of the doors you didn't select (and eliminating one that Monty knew was wrong) he's offered you the chance to switch your odds from 1/3 to 2/3. So you should switch.
What? He eliminates a wrong door that you don't pick. So the odds go immediately to 50/50. Making a change at that point doesn't change your odds at all.
