Here's a little conundrum that someone asked me the other day and it really demonstrates the power of the exponential.
If you have a 64-square chess boards and an infinite supply of coins (if only) that are 1/8" (3.175mm) thick, and you placed 1 coin on the 1st square, doubled it and placed 2 coins on the 2nd square, doubled it again and placed 4 coins on the 3rd square, doubled it again and placed 8 coins on the 4th square, doubled it again and placed 16 coins on the 5th square, and continued doubling thereafter...
...How high would the pile of coins be on the final square?
Now the trick here is to have a qualitative guess at the height, for example "as high as my house". Don't use software or maths to calculate the height, because that defeats the point of this.
Dave
If you have a 64-square chess boards and an infinite supply of coins (if only) that are 1/8" (3.175mm) thick, and you placed 1 coin on the 1st square, doubled it and placed 2 coins on the 2nd square, doubled it again and placed 4 coins on the 3rd square, doubled it again and placed 8 coins on the 4th square, doubled it again and placed 16 coins on the 5th square, and continued doubling thereafter...
...How high would the pile of coins be on the final square?
Now the trick here is to have a qualitative guess at the height, for example "as high as my house". Don't use software or maths to calculate the height, because that defeats the point of this.
Dave