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posted
N[(Sqrt[2] + Sqrt[3])^100, 286] = 6.01896 × 10^49
6 i think
posted
hue I'm fool
60189565958534864246850581634349698760897425062497
ok I think neta wins
posted
I have no idea about this.

Maybe i'm wrong or not. it's too hard question
posted
ok next game~~

Trying to find out which maps the following three screenshots comes from!

each one may post only once, and no edit allowed!

the first one whose post is completely correct will win a ticket!

for pattern case, you must post DIFF link or MAP link with Correct Diff Name





posted

Neta wrote:

it's (√2+ √3)^100 so we should find integer first

(√2+ √3)^8 is 9602. so (√2+ √3)^8 's digit is 2.

and 2^x 's digit goes 2, 4, 8, 6, 2, 4, 8, 6 .....

so (√2+ √3)^96 is 6.

and (√2+ √3)^4 is 97.9897....

(√2+ √3)^96 = 6

6[(√2+ √3)^96's digit] * 97. 9897[(√2+ √3)^4] goes 587, 8382....

so digit is 7

Answer : 7
not the best way but pretty close so answer accept
posted
posted
https://osu.ppy.sh/s/84014
First one, Extreme diff.

https://osu.ppy.sh/s/53451
Second one, Storyboard.

https://osu.ppy.sh/b/54581
Third one, Insane diff.
posted

Priti wrote:

https://osu.ppy.sh/s/84014
First one, Extreme diff.

https://osu.ppy.sh/s/53451
Second one, Storyboard.

https://osu.ppy.sh/b/54581
Third one, Insane diff.
that it is
posted
here's some fix about solution.

(√2+ √3)^8 is not integer i got rounding off to the nearest integer
posted

Neta wrote:

here's some fix about solution.

(√2+ √3)^8 is not integer i got rounding off to the nearest integer
if you don't round you get a completely different answer but the unit digit is still 7 I think
posted
I finally give up this one
In spite of 0 pending map, I still want to make it somehow, which turn out to only ask me for trouble.
hopefully Millihiore will come along with the task
posted

Frostings wrote:

if you don't round you get a completely different answer but the unit digit is still 7 I think
Not a completely different it was almost near to integer. so actually digit doesn't change if i multiple 12 or not

anyway it was my mistake
posted

Frostings wrote:

Neta wrote:

here's some fix about solution.

(√2+ √3)^8 is not integer i got rounding off to the nearest integer
if you don't round you get a completely different answer but the unit digit is still 7 I think
that it is, that's why i call his solution is a "tricky way"
posted

Scorpiour wrote:

Frostings wrote:

here's some fix about solution.

(√2+ √3)^8 is not integer i got rounding off to the nearest integer

if you don't round you get a completely different answer but the unit digit is still 7 I think
that it is, that's why i call his solution is a "tricky way"
But the unit digit of something rounded is not always the same as the unit digit of the number itself.
Take 7.75. It's unit digit is 7 but if you round it, you get 8.
I'm not sure i follow the logic here.
posted

rezoons wrote:

But the unit digit of something rounded is not always the same as the unit digit of the number itself.
Take 7.75. It's unit digit is 7 but if you round it, you get 8.
I'm not sure i follow the logic here.
That's why i pick (√2+ √3)^8. my solution doesn't follow logic when the sing of decimal is over 0.5 because it makes digit goes up like you said

and it should be really close to integer to find right digit answer
posted

Neta wrote:

rezoons wrote:

But the unit digit of something rounded is not always the same as the unit digit of the number itself.
Take 7.75. It's unit digit is 7 but if you round it, you get 8.
I'm not sure i follow the logic here.
That's why i pick (√2+ √3)^8. my solution doesn't follow logic when the sing of decimal is over 0.5 because it makes digit goes up like you said

and it should be really close to integer to find right digit answer
Ok, so if i understand your logic.
(√2+ √3)^8 is nearly equal to 2. So you deduce that the unit digit of (√2+ √3)^8x is the unit digit of 2^x

(√2+ √3)^8 is 9602. so (√2+ √3)^8 's digit is 2.

and 2^x 's digit goes 2, 4, 8, 6, 2, 4, 8, 6 .....

so (√2+ √3)^96 is 6.
Problem is (√2+ √3)^16 is aproximately equal to 92198402.03 and it's unit digit is 2 and not 4 according to your reasoning.

So, i still don't understand.
Sorry if i keep insisting but my computer calculate 8 as the unit digit of (√2+ √3)^100 so i'm still not 100% satisfied. I'm really curious about what was Scorpiour's proof.

We solved everything by PM. I was wrong. Sorry for all the post in the queue.
posted

rezoons wrote:

So, i still don't understand.

Sorry if i keep insisting but my computer calculate 8 as the unit digit of (√2+ √3)^100 so i'm still not 100% satisfied.
Are you sure you put √2 and √3? nah you didn't maybe

It doesn't matter if your computer calculate 8 or 7. because √2 and √3 doesn't end it's limitless. so it can be 7 and it can be also 8.

here is not Math queue so we'd better stop talking about this here

please PM to me if you can't understand



EDIT : if is there someone think my answer is wrong. here's site for you

http://www.wolframalpha.com/

word : (sqrt(2)+sqrt(3))^100
posted
New Games is about time ~~
posted
First game :

try to find out which maps these three screenshots come from, you should list all three correct beatmap links, also you may not edit the post.

the first one who post the correct answer will win a modding ticket





posted
first one: https://osu.ppy.sh/s/30266 Yue's dff

2nd: https://osu.ppy.sh/s/55000 Paradise Kiss' diff

3rd: https://osu.ppy.sh/s/96338 HW" diff
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