Good point. I think the easy way to do it would be to double the cost of the last and subtract one.

(2^(n-1) * 2)-1 = (2^n) -1
(2^32) -1 = 4294967295 (cents)
$42,949,672.95, which agrees with your results.

Edit: I made a typo.

$42,949,672.95

That's more like it. This is reminiscent of the puzzler about the wise ass who had some king pay him a penny for the first square on a chess board and two pennies for the second, four for the next, and so on doubling the amount until the King figured out what was going on and had the guy beheaded.

You will have to wait for another nut until tomorrow, but I will off this little puzzle from another, unrelated book.

"How I need a drink, alcoholic in nature, after the tough chapters involving quantum mechanics!"

Glatt, a heroic calculation !

But the answer depends on your assumption about "first nail"
1st leg: 1st nail = $0.01 ... 6 nails per shoe = $0.63
2nd leg: 1st nail = $0.01 ... 6 nails per shoe = $0.63
3rd leg: 1st nail = $0.01 ... 6 nails per shoe = $0.63
4th leg: 1st nail = $0.01 ... 6 nails per shoe = $0.63

Total: $2.52
Time to calculate: 15 seconds :D

4 hooves, 8 nails per hoof = 32 nails
2 to the 32 = $42,949,672.95

that's embarrassingly easy. I'm ashamed that I pulled out my calculator to add all those nails up. I should know better.

Edit: Wait a second. That's wrong.
Attachment 36375

He left out the "minus 1."

An my plan would have worked if it hadn't been for that meddling Jesus!

Today's nut brought to you by Squirell Nutkin!

The squirrel is on the tree, and he went around the tree, so yes, he went around the squirrel.

Does Jupiter go around the Earth?

Is there a treadmill involved?

Does Dark Matter surround Uranus?

This one messes with my space/time/direction dyslexia. I'm sure this ties into my objection to the 'lefty loosy righty tighty' adage, too.

If the squirrel were avoiding the dude in the same direction around the tree, how is he going around the squirrel?

The squirrel is not part of the tree, he's just on the tree.

What if it's a really big tree and the hunter is on the inside?

That hunter's so fat that when he sits around a squirrel, he really sits around a squirrel!