N[(Sqrt[2] + Sqrt[3])^100, 286] = 6.01896 × 10^49

6 i think

6 i think

show more
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**

#### Neta wrote:

http://osu.ppy.sh/b/54581 INSANE

http://osu.ppy.sh/s/53451 storyboard

http://osu.ppy.sh/b/110915 extreme
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.
#### Priti wrote:

#### Frostings wrote:

#### Scorpiour wrote:

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.
#### rezoons wrote:

and it should be really close to integer to find right digit answer
#### Neta wrote:

(√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

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.
#### rezoons wrote:

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
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

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
show more

Joined **November 2011**

N[(Sqrt[2] + Sqrt[3])^100, 286] = 6.01896 × 10^49

6 i think

6 i think

Joined **March 2013**

hue I'm fool

60189565958534864246850581634349698760897425062497

ok I think neta wins

60189565958534864246850581634349698760897425062497

ok I think neta wins

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

it's (√2+ √3)^100 so we should find integer firstnot the best way but pretty close so answer accept

(√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 7Answer : 7

Joined **May 2011**

http://osu.ppy.sh/s/53451 storyboard

http://osu.ppy.sh/b/110915 extreme

Joined **December 2012**

First one, Extreme diff.

https://osu.ppy.sh/s/53451

Second one, Storyboard.

https://osu.ppy.sh/b/54581

Third one, Insane diff.

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, that's why i call his solution is a "tricky way"## Neta wrote:

here's some fix about solution.if you don't round you get a completely different answer but the unit digit is still 7 I think

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

rezoons

But the unit digit of something rounded is not always the same as the unit digit of the number itself.## Frostings wrote:

here's some fix about solution.that it is, that's why i call his solution is a "tricky way"

(√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

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.

But the unit digit of something rounded is not always the same as the unit digit of the number itself.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

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.

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

rezoons

Ok, so if i understand your logic.## rezoons wrote:

But the unit digit of something rounded is not always the same as the unit digit of the number itself.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

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.

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

(√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.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.

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

so (√2+ √3)^96 is 6.

So, i still don't understand.

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

So, i still don't understand.Are you sure you put √2 and √3? nah you didn't maybe

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.

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

try to find out which maps these three screenshots come from, you should list

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

Joined **February 2011**

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

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