Originally posted by Alcranot so fast....
if the question was of the form "
is the last digit of the answer to 2^2006 = 8" and you had no idea whatsoever as to the answer, then a betting man would say "no" - since there are 10 different digits the last number could be (0-9).
😉
His only answers to the question "does it end in an eight" are YES and NO. 2 answers....so therfore he has a 50/50 chance of picking the right answer!
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Originally posted by Knight Squareyou can also work it out using modulo arithmetic. if we use modulo 10 then this says we're only looking at the last digit. 3*4=2 mod 10 as the last digit of 12 is 2. this holds for all natural numbers (and others, but that really doesn't matter here...)
This a very simple question. What is 2^2006, is the last digit 8? See I am a very stupid and dumb person so please if you do insult me, it just won't work. Okay I have already come to that reality, everybody has told me.
2^2006 mod 10
=(2^2).(2^17).(2^59) (that's where long division-or a graphics calculator-come in handy...)
=4.(2^17).(2^59)
the last digit of 2^17 is 4 as we know that 18 is divisible by 3 and this the last digit of 2^18 is 8. 8/2=4. we can also work out 2^59 mod 10 this way.
thus,
2^2006 mod 10=4.4.4 mod 10=6.4 mod 10=4 mod 10.
this method is really kinda time-consuming here, but for other numbers it's more useful. i worked it all out then realised that actually it was a much simpler question and we didn't need mods. ThudanBlunder's method is simpler and easier (and quicker...) here🙂 but i'd worked it all out, and spend a good 5 mins trying to remember how to do it all. so i decided not to let it all go to waste... 😛
The least significant number in the series of numbers follows the pattern
2, 4, 8, 6, 2, 4, 8, 6 etc. There's no need for all this complex furmulae to work this one out surely.
2004 is divisible by 4 so it follws that it will be the fourth number in the series ie 6. Hence 2^2006 ends in the second number along in the series ie 4. [fanfare][/fanfare]
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Originally posted by BowmannI have been offline since returning to the UK from China six months ago. I used to live in Camden, London but now live in Morecambe. You have probably passed through it, but didn't notice. If extraterrestials beamed down to Earth I reckon they would hide away here, just to be on the safe side.
So, where have you been all these months? Maternity leave?