if you place a penny on the 1st square of a chess board and double it each square, what is the final total?

Question

in words as well as figures please.

Answer 1

When you double the number of coins for each square, you leave yourself one coin short of a total of 2^n (two to the power of n) coins where 'n' is the number of squares. Try this & see:

For four squares, you'd have 1+2+4+8=15 coins. 2^4=16, and 16-1=15. If you look at other numbers you'll see the same result - total = 2^n-1.

Since a chess board has 64 squares, your total would thus be 2^64-1. Most computer-based spreadsheets & other software can't display numbers to the required degree of accuracy since the answer is in fact 20 digits long.

If you have a calculator, a pen & paper and some patience, you can work with smaller numbers to build a bigger picture. 2^16=65536, this can be squared (multiplied by itself) to give 2^32 which is 4294967296. If you break this up into two five-digit numbers, i.e. 42949 & 67296, you can multiply these in much the same way as you would multiply two two-digit numbers. The result is 2^64=18446744073709551616. Since your final total of coins would be 2^64-1, your final number of coins would be 18,446,744,073,709,551,615.

Incidentally, the pile on the 27th square would be officially into space, that on the 39th would reach the Moon, the 48th would go beyond the Sun, and the final square would hold a pile reaching nearly one third of the way to the next star after the Sun.

You'd also need to be extremely rich!

Answer 2

When you say the final total, do you mean on the final square? If that's the case, then the answer is 2^63, which is an ENORMOUS number: 9.223372037 * (10^18)

This is because the number is doubled sixty-three times. The sum of all the pennies on the board is 2^64, minus the one penny, since the first wasn't doubled. That is 1.844674407 * (10^19)

Answer 3

a chess board is an 8 by 8 square. 64 places total.

the equation is going to be the sum of 2^n from n=0 to n=63 (since we start with one. 2^0=1)

1+2+4+8+16+32+64+128+256 etc...

Answer 4

The United States and the UK have different definitions for large numbers so it depends on which system you were schooled in.
US - Billion = 1,000 million (9 zeros after the 1)
UK - Billion = 1 million, million (12 zeros after the 1)

Therefore by the US definition it would be a total of Ninty-two quadrillion, two hundred and thirty-three trillion, seven hundred and twenty billion, three hundred and sixty-eight million, five hundred and forty-seven thousand, eight hundred pennies.

And by the UK definition it will be Ninty-two billiard, two hundred and thirty-three billion, seven hundred and twenty milliard, three hundred and sixty-eight million, five hundred and forty-seven thousand, eight hundred pennies

92,233,720,368,547,800

Answer 5

2^64-1 which is approximately 1.844674^19 or

18446744073709551615 to be exact

Answer 6

More than all the grains of sand in the world.

Answer 7

get a pencil and piece of paper and work it out yourself/it will be a huge amount

Answer 8

$37
....

Answer 9

18,446,744,073,709,551,615