Haven't published in ages, so let's have a few warm-up questions over the next days.
Question
Find the last two digits of 20182018
(If you cannot see the superscript, this is 2018^2018.)
This is supposed to be done with just pen and paper; the actual number is too large for most programs anyway.
The first correct answer and further interesting comments will be rewarded with an upvote.
Enjoy!
More Brainsteems coming soon...
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This is a quick solve -- it reduces to finding the last 2 digits of 182018, and the last 2 digits of powers of 18 start with 181=18, and then go into a pattern of 24, 32, 76, 68, 24, 32, etc.
The cycle length is 4, the last 2 digits of 182 is 24, and 2016 is evenly divisible by 4, therefore the answer is 24.
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Only the last two digits of each multiplication by 2018 contribute to the last two of the result, so I would hazard a guess that it would be similar to 18^2018...now to work on reducing the power.
Seems to repeat every 5th power, so I put in 68 as the last two digits?
This is tricky to do while juggling kids...
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You can juggle kids? That we must see!
They must have been distracting, as nearly there, but the first power isn't in the cycle of numbers.
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Lol... Oops, that would be the kiddie distraction part! I did notice that, but I think I started counting wrong...
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