Brainsteem Mathematics Challenges: Powers of 2018
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!
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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.
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...
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.
Lol... Oops, that would be the kiddie distraction part! I did notice that, but I think I started counting wrong...