My contest was What is the biggest number you can make with three different digits.
Obviously you should use the digits 7 , 8 & 9. But how do you have to order them?
- just writing one behind the other would result in being 987 the biggest one.
But that's is not the biggest one you could make. Don't forget raising it to the power of...
So let's try 9^8^7 = (9^7^8) = 2.7389 * 10^53
Well yes that's a lot more than 987
But is it the biggest one? Well, it is the biggest one with the biggest basis. But most time more important than the basis is the exponent. So we should try to maximize the exponent:
8^9^7 = 8^(97) = 8^63 = 7.84610^56
7^9^8 = 7^(98) = 7^72 = 7.03210^60
But that is not the biggest one yet: You could also combine these two possibilities (raising to the power & writing one behind the other):
9^87 = 1.04510^83
it's having the biggest basis but the lowest exponent, so this isn't the biggest number you can make with three different digits. So we try to improve and maximize the exponent:
7^98 = 6.610^82
What it's even lower than 9^87!? So 9^87 is the biggest one? - No, the basis is not completely unimportant. So let's try 8^97:
8^97 = 3.9810^87*
Congratulations to @drvnpatel who has been the first one who wrote the right answer. SBD are on their way!
Thanks a lot @valkyrion in Anticipation.
I love to participate in such contests.
I am glad that I am chosen as a winner, and thanks for the detailed explanation of the correct answer.
Thanks a lot and I look forward to participate in more such contests.