A man from a nearby country explained the king how to play chess. Becoming very interested in the game, the king wanted to praise the man and asked him what he want. He humbly asked the king to give gold coins with the following condition.
Put a gold coin in the 1st square of the chess board and consequently put the double of the previous one's content in each squares. The total count of coins of all 64 squares placed in this order must be paid to him.
The king agreed happily to give that *SMALL* amount and he is now going to count. He is having ten tons of Gold in his treasury and a gold coin is weighing a gram. Answer me, will he praise the man as promised.
IF YOU CAN'T, THEN YOU'RE GRANTED TO USE YOUR COMPUTER.
2006-09-08 08:21:55 · 17 answers · asked by Naveen 2 in Entertainment & Music ➔ Jokes & Riddles
First of all, ten tonnes (I'll assume you did not mean tons which is an imperial, not metric, unit) is equal to 10 000 000g and therefore 10 000 000 gold pieces. The chess-teacher will get 1 coin for the first square, 2 for the second and doubled every time so that the general formula for the no. of coins for any 1 square has 2^x in it. We find it is 2^(sq.number-1) so for 64 squares he will get 2^0 + 2^1 + 2^2 etc. up to 2^63. Binary system is based on the fact that 2^1+2^2 etc up to 2^x=2^(x+1)-1 so for this example The man will get 2^64-1. Now comes the difficult bit to do on paper. What is 2^64? Note that 2^xy=2^x times 2^y so 2^64=2^16x2^16x2^16x2^16 and after some doubling twos (2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536) we find that 2^16=65536 and then after strenuous long multiplication we find that 65536*65536=4294967296 and then 4294967296*4294967296=18 446 744 073 709 551 616 take one is 18 446 744 073 709 551 615 and we get the number of coins the man should get. Take 10 000 000 and we get 18 446 744 073 699 551 615 which is what the man is still owed after the ten tonne instalment (this is 18 446 744 073 699. 551 615 tonnes). So no, the King did definitely not give the teacher the full prize.
2006-09-08 09:13:22 · answer #1 · answered by me 2 · 0⤊ 0⤋
each square from one to sixty-four gets the number of coins (N) equal to two to that square number (n) minus one.
N= 2^^(n-1)
N = 2 ^^(63) on the last square.
No, I cannot do that math by pencil and paper. I am betting he runs out of gold pretty quickly.
The total is the sum of all the squares (1-64)
T = sum(Ni) where i-1-64
2006-09-08 08:30:27 · answer #2 · answered by NeoArt 6 · 0⤊ 0⤋
Well there would probably be a new king soon after the queen found out.
After half the chess board was filled it would be up to 3,221,225,472. I dont want to go any further.
2006-09-08 08:43:11 · answer #3 · answered by Anonymous · 0⤊ 0⤋
The king doesn't have anywhere near enough gold to pay off.
2006-09-08 08:32:57 · answer #4 · answered by Dave 4 · 0⤊ 0⤋
I am getting
(2^64)-1
2006-09-08 08:32:38 · answer #5 · answered by iamigloo 6 · 0⤊ 0⤋
Poor king. it is not possible for him to pay the assured gold as promised.
Moral of the story:
.............Never promise to any body, without thinking or in a hurry.
2006-09-08 18:00:30 · answer #6 · answered by Electric 7 · 0⤊ 0⤋
(sigma 2^n where n=0 to 63) grams
convert grams to tons
I think the king will be annoyed, not to mention poor.
2006-09-08 15:14:10 · answer #7 · answered by Anonymous · 0⤊ 0⤋
If he starts from the center of the board then 2025 grams of gold he will be giving......
2006-09-08 12:20:43 · answer #8 · answered by Wanderer 2 · 0⤊ 0⤋
pencil and paper or computer, I can't figure it out. I know that it is a LOT. and not the king will not praise him as promised.
2006-09-08 08:26:43 · answer #9 · answered by Why do you ask? 5 · 0⤊ 0⤋
the king will not be able to praise the man as promised!
2006-09-08 23:54:47 · answer #10 · answered by poppadum 2 · 0⤊ 0⤋