Graphics Calculator can't work out...

Originally posted by Alcra
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).
😉

not so fast....

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!

Originally posted by uzless
not so fast....

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!

Will the sun rise tomorrow?

YES/NO

Originally posted by ThudanBlunder
Will the sun rise tomorrow?

YES/NO

no one knows if there will be a tomorrow.....

Originally posted by Knight Square
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.

you 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...)

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... 😛

Originally posted by uzless
no one knows if there will be a tomorrow.....

Toss a coin then.

Originally posted by SPMars
Although Mathematica is good, it's also quite expensive.

Then get it for free.

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]

Originally posted by Bowmann
Then get it for free.

Advocating piracy Bowmann?

Originally posted by XanthosNZ
Advocating piracy Bowmann?

Infer what you will.

Originally posted by ThudanBlunder
Will the sun rise tomorrow?

YES/NO

That depends on where you are.

Originally posted by Bowmann
That depends on where you are.

Says Bowmann in a muffled voice with his head up his arse.

Originally posted by ThudanBlunder
Says Bowmann in a muffled voice with his head up his arse.

So, where have you been all these months? Maternity leave?

Originally posted by Bowmann
So, where have you been all these months? Maternity leave?

I 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.

Originally posted by ThudanBlunder
If extraterrestials beamed down to Earth I reckon they would hide away here, just to be on the safe side.

Morecambe? Wise 😵

Actually, I have holidayed there 😕