4 + 0 = 0 puzzle
HTML-код
- Опубликовано: 20 апр 2022
- Move exactly 3 matchsticks to make the two sides equal. #shorts #puzzle
Source
matchstickpuzzles.blogspot.co...
Subscribe: ruclips.net/user/MindYour...
Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2022.
My Books (worldwide links)
mindyourdecisions.com/blog/my...
My Books (US links)
Mind Your Decisions: Five Book Compilation
amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.2/5 stars on 224 reviews
amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4/5 stars on 24 reviews
amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.1/5 stars on 38 reviews
amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.2/5 stars on 76 reviews
amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.3/5 stars on 30 reviews
amzn.to/XRm7M4
Mind Your Puzzles: Collection Of Volumes 1 To 3
amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 87 reviews
amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.1/5 stars on 24 reviews
amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 22 reviews
amzn.to/1NKbGlp
2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.
My Blog
mindyourdecisions.com/blog/
Twitter
/ preshtalwalkar
Merch
teespring.com/stores/mind-you...
Patreon
/ mindyourdecisions
Press
mindyourdecisions.com/blog/press 
Наука
Wow, you guys have found many solutions I overlooked! These are great!
3 + 8 = 11
-4 + 8 = 4
-4 + 6 = 2
11 x 0 = 0
Can you find any others? Valid solutions move exactly 3 matchsticks and make the two sides equal.
4+5=9¹
I did 1/1 + 0 ≠ 0
I also did 4 + V = 9 because the V is the Roman numeral 5.
1/1 + 0 ≠ 0 ---
Moved 2 of the match sticks on 4 that is not the middle one to form 1/1. Then, used the last one that is not the middle match to make the ≠ symbol.
4 + V = 9 ---
Moved the top and bottom matchsticks on the first 0 to make a V. Then moved bottom right matchstick of the second 0 to the middle of the second 0.
+4 + 0 = 4
I can move exactly 2 matchsticks. Make 9+0=9 why three?
4×0=0
If you're willing to move a match stick somewhere and back.
Turn the plus sign so that it is multiplication, and then move the middle stick from the four.
It changes to 11*0=0, which is true.
That's what i was thinking
EXACTLY
two exact moves to create the multiplication sign will make any # on the left = 0
Second solution with the same idea:
-Rotate the plus sign to get the multiplication sign
-Instead of moving the matchstick to make 11, move it to the top:
7*0=0
@@kytonchan2036 That’s true, but the task was to change the equation by moving *exactly* three matches.
Me: transforms + to - and = to ≠
ME TOO LOLLL
≠ be like: am I a joke to you?
he said make the two sides EQUAL. not make the equation true. you dont know what equal means?
Another solution would be the following: we move the top right stick of the LHS zero to its middle, transforming it into a 6; then, we do the same with the top left stick of the RHS zero; finally, we move the bottom right stick of the RHS zero next to the four, rotating it 90 degrees. This way, the equation we obtain is -4+6=2
Great.. solution dear
That is beautiful!
I came up with 9-0=0
@dmar oops I meant 9-0=9 my bad 😂😂😂
3+8=11??
NICE. The video says there are only two. You proved that there is at least three, not counting the multiplication answers.
Exactly my thought
@@dimpufrn8201 yeah came here to write that too
That's the one I found too.
@@nathanmays7926 why not the multiplication tho, they are correct as well
I can do it in 1. Move the vertical stroke of the + to the equal sign and make: 4-0≠0, easy😎
Damn it, you beat me to it xD
Good job!
Nope, if you listen closely, he says the two sides have to be equal, not that the equation has to be true.. had the same idea to use >,
He said exactly 3
@@LinusSegueRatings You got me good
He said 3 not 1
Him: “Move three sticks”
Me: “Turns the + into an x”
Thats 2 sticks
@@person2269 that’s the point, I did it in less
In one, take the vertical part of the +, move it to the equal sign and make it ≠ then it’s 4-0≠0
@@CircCat thats the point, there are many solutions eith moving 2 match sticks that are easier than 3... You're supposed to kove exactly 3, because that makes it harder
@@phobiaAOE no i was just pointing out that they were trying to make it seem like a greater accomplishment to do the challenge in less moves than it had stated. But that's the thing that makes it hard, having to do it in more moves
Make the four look like this: “4” and then move the “+” to a “x”
I got 4+0=4 by removing 3 matches from the 0
You did the same thing as me
@@katincko you are only allowed to move three. not one, not two, not four, etc.
He said to move only 3 Matches, didn't specify the number only 😉
Thats what i thought XD
Move the middle match of 4 to the lower left and take both + matches to turn the 4 into a 0.( 0 0 = 0 )
That one is great
@@stormfox2907 Appreciate it.
Move the + sign and then turn the 4's middle matchstick around. It becomes 11x0=0, which is correct.
You could move the vertical stick in the + to the equal sign so that it would be 4-0≠0.
You solved it in 1 move
“Exactly three@
I think I’ve got another one; rotate the plus sign 45degrees (counter or clockwise). That’s the first two moves. The third will be taking the horizontal piece from the 4 and placing it vertically on the left. This makes the equation 11x0=0
I was thinking just about the same thing, but instead rotate the top left one in the four 45degrees to make it like '4'
@@Ben-dl3zj or move the horizontal piece to top and so it is 7 * 0 = 0
thought of this as well!! I came up with:
11×0=0 and 7×0=0
for the 7, just move the same horizontal match on top lol
You don't even have to move the middle stick, just leave it as 4 x 0. You solved the problem in LESS moves than the limit allocated, which means you outsmarted the designers and now YOU'RE their boss.
@@MisterZimbabwe The rule is that you must move exactly three matchsticks.
Am I wrong or 1 + 9 = 10 and 3 + 8 = 11 are other 2 solutions?
you're right
Ya
And 11x0=0
Yeah but I'm not sure we can go in the double digits
@@CanadianSpaceBoy why?
If you can remove match sticks completely, you can also do 7+0=0 and 4+0=4.
Here's 1, move the top matchstick of the first 0 down to the middle, then move the bottom left matchstick of the first zero to the middle of the second 0, and then move the bottom matchstick of the first 0 into the backrooms making the equation 4+4=8
9 + 0 = 9
That’s what I did
4 + 0 ≠ 2
Move the top left stick of the second zero onto the equal sign. Move the bottom stick of the second zero to the middle of that same zero, and then move the bottom right stick of the second zero to the bottom position
You can make it true in two moves, just convert the plus to times
The Smith is strong with this one
I found 2 separate ways, but they dont require u moving 3 matchsticks.
1st is making 4+4=4 (u get one extra match so just throw that away)
The second and the easiest is to take a match and make the equals sign into unequals
Other solution : move the top stick of the last 0 to make 4 ; then with the 2 last stick we need to remove to make the 4 we make l4l : l4l + 0 = 4
You would need 2 sticks for each absolute value sign , each stick only covers 1/4 what you need
You could also use the 2 last stick to make -4+0=-4
@@blurr1903 its cooler than 4¹+0=4¹
In Yoda voice: "there is another"
Move both sticks in the + sign and the one in the middle of the 4 to make 00=0
Thats what i did
Same
if that works the 1 + 0 = 01 is also valid and only moves two sticks
Same
I was messing around with the signs, I made the first one 4 - 0 ≠ 0
Then the other was 4x0=0
Damn I thought it said 2 matchsticks and I found only one solution moving 2 matchsticks. The solution i found is 9 + 0 = 9
You can still get 9+9=0 with three sticks. Turn the + into a - and add one stick to the top of the 4.
then, take the bottom left stick of the last 0 and make the - a + again. Then, move the bottom stick of the last 0 into the middle.
Also 4 x 0 = 0
Can you not get 4+4=8 with just two moves?
@@Ro99 that would be impossible unfortunately
@@supportive_comment oh yeah you need to move a bit more than 2
4-0≠0
That doesnt make them equal clown
@@ebenezer-scrooge exactly ≠ symbol means doesn't equal which is correct
@@tac0811 the question was "how can you make this equation equal" but you made it true not equal
Bro you moved one
Flip it upside-down, then rotate the 2 matchsticks on the "+" to turn it into "×" then turn the upside-down 4 into a normal 4
Move 2 matches from the rightmost zero to make the first zero a zero with a line through it. Move last match to make a 4 in the last slot.
Use a match from the + symbol to make it -
Add the taken match to 4 to make it thrumbo and move last two matches on the rightmost zero to make another thrumbo.
9 + 0 = 9 (moving 3 matchsticks)
1) take any from the middle 0, place on top of the 4 to make a 9
2) take bottom left “leg” from the 0 on the right, replace the slot from step 1
3) move bottom from 0 on the right up to the middle to make a 9
(I admittedly strain the meaning of the question’s prompt, but it did not exclude this strategy)
4 - 8 ≠ 5
In the video he says that you have to make the both sides equal so that doesn't count
That does count though
@@pee0001 nah it specifies to make the two sides equal, not to make the equation work.
@@fgvcosmic6752 Exactly
True answer or not, it's still a valid statement with 3 matches moved. Gotta give him credit for coming up with it at least
I actually found another solution: move both the matchsticks in the plus sign to the 4 and turn it into a 0
00 = 0
Am I missing something? You have to put 3 matches onto the 4, but you are only taking 2 out of the +.
@@MegaSuperEnrique no it's still 3 steps though as you have to move the middle horizontal stick to up and the two sticks of the "+" symbol to there respective places to form a zero from "4".
It's 3 steps. I didn't include it in my list because nobody would ever write 00.
i came up with the same solution lmao
I solved it this way too
Another way is to take the match at the top from the = zero and take the bottom from the same zero and set to the side and take the bottom left from the same and place it in the middle of the zero and now its a = four
Just take one from the plus sign and then it will turn into subtraction and you can use that one to make a not equal sign lol
1 + 9 = 10
Damn another one
4 x 0?
you need to move 3 that's only 2
@@resied4620 If you move one of the matchsticks that make '=' up or down it will mean you have moved 3 matchsticks technically. (even though it didn't alter the equation)
0*0=0
-1 + 9 = 8
First move middle match in 4 to 2nd 0 to make 8, then move the isolated matchstick wherw the 4 was to make -1 then move bottom left match on the middle 0 to make 9
-1 + 9 = 8
Or you can solve by moving one. by removing one from the (+) sign, and adding it to the (=) sign. to make a (not equal sign). Making the two sided unequal and the equation true.
I came up with a COMPLETELY different answer 😂😂😂
Is it 0 0 = 0
I moved the top one of the plus and made a not equal to lol
I made the second 0 into a 4
After I took one of the sticks of of the plus
Same
Me: so you take the inside of the 4 and make it a line with the one match. Then, you use the matches on the plus to turn it into a zero. 00=0
Same thoughts
same here
same
Me: moves the stick going vertical in the + and putting it over the = sign to make the does not equal sign
This one too*
*So 4+0=0, right?
_So my answer is-
4-6≠6
====================================
---------------------------------------------------------------------
-------------------------
Move the match from "+" and cross it to the equal "=" making it "≠", then in the "0" take the match from the upper right then put it on the middle of "0", and then do it on the other "0" too.
Hehehe😊
The real trick is to drive engagement by making it so easy that people comment there own answers.
you can move a stick from the 4 to turn the 4 into 11 and turn the + sign 45º to make 11 x 0 = 0
Or only turn the plus - that is a solution with two moves
you can move a stick from 4 and turn to 11 then put the vertical match of plus to the top of 0 and the match original on top of 0 between 1 and 1
@@corn1002 I wouldnt count replacing 2 matches (vertical one in the + and the top one on the 0) as moving them since they are identical but 1-1-0=0 is a rly great idea if i didnt get your comment wrong lol
@@ghasmiller That does not count. You must do it with three moves of three different matchsticks.
my solution: move the top left match on the four so it looks like this "4" then change the plus to a times
This is so wrong because there are more then two possible answers the one I came up with is 1+8=9 by moving two from the four and make a one like this font uses then take the other one put it on the 8 and use you last move to make the 0 into a 9 by moving the bottom left stick of the zero
Or 3x0=0
@@Yaboijoe33 where do you put the third match? You take two matches from 4 turning it into 1 use one match to turn first 0 into 8 and then move one match from the second 0 to turn it into 9 leaving you with a match at hand.
How about 00=0?... Yes, there is a space in between the 0s, but here is 1 step-by-step breakdown:
1. Move the matchstick in the middle of the 4 up, such that it reads like this: '7.
2. Integrate the plus sign into the distorted 4, by 1st moving its vertical bar into the '7 shape for an n-shape, and then moving the horizontal bar below the n to make the leading 0.
There are multiple other ways to go about this.
0-0-0 (i understood 'equal' as symmetrical)
Move middle stick from 4 to make 11. Then take the vertical stick from the + and one from the = and place them on the top n bottom of the now 11 to make 0.
Everyone coming up with smart solutions
Me: moves the plus sign onto the four and make the four a zero
00 = 0
That’s what I found too
That is also exactly what I did when I saw the thumbnail. 00 = 0
Your not lazy for picking the lowest fruit just reserving your potential and possibly smart
I thought of that too lol
same
What about - 4 + 8 = 4?
4 - 8 ≠ 5
That's 3 moves, and it's a true statement.
@@calholli but it's not equal
@@vipereleol6307 Right.. the symbol I used says it's not equal. Maybe you're seeing it, being an emoji that doesn't render of something: but it's an equals sign, with a slash through it.
@@calholli no he means that the person says that they have to be equal. your making the equation true, but not making it equal
@@elynmartinez4896 who makes these rules anyway? lol
Move the + into a × and you get 4×0=0
But if you want to use 3 moves then make the 4 into an 11. Then you got 11×0=0
Another solution
Move the stick from 4 and place it either down or up and get the vertical stick from + turning it to - then move if to 4 now you have 0-0=0
4 - 0 ≠ 0
Take 2 from the + and put them into the 4, move the middle one to the other empty spot and you have
00=0
That's how my brain also decided it worked
It is how I did it
Move 1 stick of + sign making it minus so add it to 4 making it H now, in lhs move 1 stick from up to center 1 stick remaining take it to lhs and build + sign H+0=H
@@icyy9864 I see what your doing algebraiclly but Im p sure its asking for constants, so no variables
@@SirD3fault the question just asked to make the two sides equal by moving only 3 matches nothing else nothing more which my answer fulfils else you are free to think anyways
@@icyy9864 both of those H's could've easily been made 9's lol
9-9=0 one nine will have a longer bottom, but it still counts lol As a bonus you only need to move to sticks
Make its 0 0=0
When 2 numbers with no symbol as In +-÷ it is multiplication
It can also be 9 - 0 = 9 but one "9" would be with the stick at the bottom and another without.
Or just have 9+0=9
@@baker_boi_37
How? I can't find any way it could be done in 3 moves.
@@egosumfedchenko I did it in 2 oops
Turn the Plus into a times
i came up with 4+5 is not equal to 8:
step 1. remove a matchstick from the plus sign and add it to the equals sign to make the not equals sign
step 2. move the upper right matchstick of the first "0" back onto the plus sign so it becomes a plus agains opposed to a minus
step 3. move the bottom left matchstick of the first "0" (which is now more like a "6") into the middle of the second "0" to make an "8"
My solution is 3 + 8 = 11
Same
Yup
0-0=0
Nah m8 when you do that it's just 00=0
I found 1 + 9 = 10 as well. To do so, transform the '4' into a '1' and use the remaining sticks to create the '1' on the right hand side. Then, move one stick to transform the middle '0' into a '9'.
Make the (+) into an (×) and the 4 into an 11
I thought of 3 other solutions, admittedly one of them involved yeeting one of the match sticks into the shadow realm as the third move.
Was that solution 4+4=8?
@@scottallen4569 yes
You could also make 4+5=9 if you could remove one
@@elir626 If you remove on you can also make 4+2=6
Move the vertical stick from the + over the equal and back then move it over the = diagonally so that it is 4-0 is not equal to 0
Thats what i thought
just make the plus into a times sign only moving 2 matches
You could also do
4+2=6
Haven’t seen this one yet:
Move the top right stick on 4 to make it horizontal on top, move the top right one from 0 to the bottom of 4 (horizontal), then move the bottom left of 0 to the middle to make a 5,
And now you got 5 + 0 = 5
6-6=0
Moving two sticks makes the equation work as well, the less you move the better the method.
"The less you move the better" is not nessecsrily true, we need to make 3 moves, not fix the equation in as few moves as possible
You can do 4 - 0 (unequal sign) 0
You could also move the middle matchstick on the four down to where is equal to the other side and move two others to the top and bottom
That 5 one look like an SOS
You could also make it true with only moving 2, just tilt the + so then it's a ×
he said exactly 2
@@butast6520 exactly 3 but you could always just move a random one 180°
"move exactly 3[..]" if you throw one away with one of your moves you can do 9 - 9 = 0
My first thought was move a stick from the + to make a 9 out of the 4 . On the left 0 you can move one stick to make the plus again and one stick to make a 9 so 9+0=9
Its exactly 3 though. So that wont work.
@@person2269 it does work if your 9 is like a reversed b. This way each 9 uses 5 matchsticks and you just have to move 2 to a new postition and throw one away. But anyways there are enough other solutions
I thought of that
1 - 1 - 0 = 0
you move two left matches of 4 to the left side and then put one match between 1 and 1 from + sign
Turn upside down. Move one of the matches away in the = to make a -. Move one of the matches in + to make =. Move the match in the 4 at the bottom and join it to connect both the matches at the top of the 4 to make a 0 (looks more like a square but is still a 0!).
0-0=0
7*0=0
That way of writing 7 is only used in parts of the world, but I mean, still sounts.
Move the matchsticks in the + sign near the zero, making it X, then move the connecting matchstick in 4 to make it 11.
11 + 0 = 0 X
X = 0
Wait, where does the plus sign come from then?
@@daniel.franco the equation is 4 + 0 = 0. the + sign is there
@@itai8302 What about the x?
i haven’t looked at the solution yet but i found 9-0=9 and it just takes two matchstick moves
Move one of the sticks in the addition sign to the equals sign, making it not equal. Then, move the one of the sticks of the last 0 to make it six. Another solution: move the top stick in the first zero to the middle and remove the two sticks shaping a bottom left corner.
We can make equal by moving 2 matchstick only. Taking 1 stick from extreme right one zero and put it on four making it 9 then take another stick from the same zero and push it upward. Hence, 9+0=9
I'd say that the 9 needs to have a bottom matchstick like all do in these types of things, that wouldn't really be correct but true, it works if you count that as a 9
That's not what 9 is in the 7 segment display though
I moved the two leftmost matches from the 4 to the far right, making 1 + 0 = 01
You can do it by moving one by taking the vertical match from the addition sign and making the equal sign not equal (≠) and the equation would be 4-0≠0 which is true
Well the goal is to make the sides equal not make the equation true
That’s my solution for every single one of these equation problems
4 + 0 > 0
@@UserDoubleONine Correct doesn’t mean equal
Sh-crap
4+0=4 just move the top matchstick to the middle
and then remove the bottom and bottom left matchstick
There's actually quite a few more, if you do negatives there's a few more but it never says you can't move any of the sticks to create a "does not equal sign" so there's at least one more I found with that
7 - 8 ≠ 0
I’m a freaking genius.
"...to make the two sides equal..."
@@efisgpr Uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
4-6≠6?
Third solution :
1)move the middle stick of 4 to the top of 4.
2)then move the two sticks of + to the absolute bottom and bottom left of 4 to covet it into 0
3) new equation is 00 = 0
You can also make four by moving the top matchstick, the lower left and the bottom
Move middle of the 4 to make 11 then p it the top and bottom of the 0 on the other side as a + so you get 11+0=+11
Or, Change the 4 into an 11 as described, then rotate the + into an x
11x0=0
@@AnonymousDuckLover tbf you only need to move 2 matches in that case
@@jw5545 The + consists of 2 matches, and to change the 4 into an 11, you need 1 match. The original problem requires exactly 3 matches to be moved for the solution to be valid, so leaving the 4 as is is not an option.
You can move just one, 4-0≠0
Make it equal not unequal
I mean you can also take the assignment of "make both sides equal" too literal and make it mirrored...
So:
4+8+(reversed)4 or 4=8=(reverse)4
That would make them visually equal.
Rotate the + so it looks like a multiplication sign
Move the two left matchsticks on the 4 to make a 1 after the equals sign and move a matchstick in the first zero to make it a 9.
1+9=10
There are TONS of solutions to this. I found 2 and neither were in this video.
Wow I found 4 ways but this wasn't one of them, I liked this a lot better than my solutions tbh
@@kittycat6007 What were yours? I have another comment where I'm collecting solutions.
@@Sam_on_RUclips I looked up a lot of comment and pretty much everyone thought the same as me lol, 9-9=0 one is definitely are guable but 11x0=0 and 3+8=11 seems pretty valid
@@kittycat6007 I came up with 3+8=11 also (someone else thought of it first, but I found it independently). But I don't think 9-9=0 works. You need 2 different fonts for 9 and you only move 2 sticks. You can move 2 and remove a 3rd.
@@Sam_on_RUclips you can move 3 too, just change the fonts between each other with the match on the bottom lol. The thing is there is no rule about fonts and who cant tell thats a 9 when its made with 5 or 6 matches, so it should count too 🥺 and i don't thing removing counts as a move bc you can make 4+0=4 if you remove 2 and move 1
I mean you never specified that we HAVE to use all the match sticks in the answer. Since its not a rule, we can leave some on the side. So we can do 4+2=6, 4+4=8, and can even just change the last number so it is just 4+0=4, among many other solutions. If youre gunna make a puzzle like this, you NEED to account for loopholes.
By taking out matchsticks you are still moving em though
@@DarthNightmareNL exactly. You move some and remove others, up to 3 moves. What you do in those 3 moves are entirely unrestricted
@@pyromaniac000000 no... thats more than moving 3 matchsticks.... you want to reMOVE matchsticks...
Remove 3 move none, remove 2 move 1, remove 1 move 2, remove none move 1.
It ain't rocket science my man
@@DarthNightmareNL do you even think before you speak? My guess is no.
In 2 moves you can make it true by making it 4 × 0 = 0
Turn the + 45degrees to make a ×.. move the horizontal member of the 4 to the top to make a 7. 7×0=0
4-3=01
Not fair
@@c-lay9979 It is not a standard answer but the equation is still true
I did 8 = 1 - 9
1+0 = 01
-4 + 8 = 4
Also -4 + 0 = -4
00 = 0, move the plus sign sticks to the bottom and top of the 4. Pivot the center stick of the 4 to be the bottom left segment of the new 0.
My mind for some reason went with something like "1+0=01", but then struggled with the final matchstick
I can do it with just 1 match.
Move the vertical match from the + and turn the equation into
4 - 0 ≠ 0
Take the "+" matchsticks and move them to the to and bottom of the four, then take the machstick in the middle of the four and put it to the wall to make 00=0
That was my solution too
Move two from the 4 to make a 1, place them next to the second 0 to make 10, and rotate the lower left stick of the first 0 to make 9. It'll read 1+9=10
I changed the 0 after the equation into a 4. Move the bottom stick to the middle. Then remove the left bottom stick and the top stick
Move the top stick in the 2nd zero to the middle, then take the bottom left two away to make it 4. Take those two matchsticks and put them inside the first zero to make it 0 with a slash inside. :)