See, now the problem with that sort of puzzle is that there's no consistency. It's true that
9^9^9 > 999
However, I'm pretty sure that
999! > 9^9^9
Think about it...9^9^9 = 387420489^9 = 387420489*387420489*387420489*...*387420489
But if I consider a sequence of multiplications in 999!, say
899*898*897*896*895*894*893*892*891 = 3.6x10^26
Then there are more than eight other sequences larger than this one -- such as the next nine numbers up, the next nine numbers after those, and so on. So if I multiply just those nine sequences together, I get a number much, much larger than 9^9^9 already. And there are far more numbers to multiple to get to 999!
So 999! is, unless I am really mistaken, a much, much larger number than 9^9^9. But why doesn't it count?
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Mohan
After all these years, in the midst of the desert, the boy child still weeps....
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1.Have someone pick a number between 1 and 9.
2.Now have him use a calculator to first multiply it by 9, and then multiply it by 12,345,679 (notice there is no 8 in that number!).
3.Have the person show you the result so you can tell him the original number he selected!
How? Easy. If he selected 5, the final answer is 555,555,555. If he selected 3, the final answer is 333,333,333.
The reason: 9 x 12345679 = 111111111. You multiplied your digit by 111111111. (By the way, that 8-digit number (12,345,679) is easily memorized: only the 8 is missing from the sequence.)
Why is a ^ not a digit but a ! is a digit? They're both arithmetic operators! By your logic, 9^9^9 has five digits.
Well, fun to play anyway.
__________________
Mohan
After all these years, in the midst of the desert, the boy child still weeps....
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if you write 9 to the power of 9 to the power of 9 it's a 9, then a nine slightly above and to the right, then a 3rd 9 slightly above and to the right. There are no "^" marks in it. We only use those on computers.
Here's the next one:
Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the missing $1?
the three goes back to the original 10s
so that becomes 9 + 9 + 9 = 27
27 - 2 = 25 (don't add the 2, subtract it).
We have a winner!!!!
Here's the next one:
If I were in Florida and dropped a baseball into a bucket of water which was at a temperature of 45 degrees F and dropped another identical baseball into a identical bucket of water at a temperature of 30 degrees F, which baseball would hit the bottom of the bucket first?