A question:

If i have a chess board and place a pound coin on the first square, and double the pound coins on the next square, how high will the pile of pound coins be on the final square ?

Using google as a reference for measurements and sizes, i thought i’d work it out… working as follows…

The correlation

Here is a table showing the correlation of the number of coins to each square..

Square # of Coins Relationship
1 1 1
2 2 1 * 2
3 4 1 * 2 * 2
4 8 1 * 2 * 2 * 2

So clearly the relationship is staring us in the face;

number of coins = n
square number = s

n = 1 * 2s - 1

The final square

So on the final square of a chess board (the 64th square), the amount of coins will be:
1 * 263 = 9223372036854775808

a quick google search reveals to us that pound coin is: 3.15mm heigh.

to the total height in mm will be:
9223372036854775808 x 3.15 = 29053621916092543795.2mm

another google search tells us how many km in a light year,
1 light year = 9.4605284 × 1012 kilometers… or 9460524840000km.

So lets convert our height in mm into km, (divide by 1 million)

total height of coins in km: 29053621916092.5437952 km

Finally, coin height in light years…

So our final calculation is:
coin height in km / distance of one light year in km = total coin height in light years.
29053621916092.5437952km / 9460524840000 = 3.0710370098338586250358600612268

Final height of the 64th square: 3.07 light years high.

Now thats impressive doubling.