What is the next number in the series: 21, 21, 23, 20, 5, 25, 31, 24,?Haselbauer-Dickheiser Test no. 3: Circle divided by lines between a blue dotsFind the next number in the series?Jumping on the BandwagonUncle's mathematics puzzles after dinnerWhat is the missing in this pattern?What is the pattern that should appear in the box?What is the pattern to appear in the box?What's the next pattern in the sequence?Which of the numbered figures fits into the empty space marked by the question mark?What's the number in the cell marked by the question mark in the cell according to the pattern?What's the number in the last cell according to the pattern?
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What is the next number in the series: 21, 21, 23, 20, 5, 25, 31, 24,?
Haselbauer-Dickheiser Test no. 3: Circle divided by lines between a blue dotsFind the next number in the series?Jumping on the BandwagonUncle's mathematics puzzles after dinnerWhat is the missing in this pattern?What is the pattern that should appear in the box?What is the pattern to appear in the box?What's the next pattern in the sequence?Which of the numbered figures fits into the empty space marked by the question mark?What's the number in the cell marked by the question mark in the cell according to the pattern?What's the number in the last cell according to the pattern?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty
margin-bottom:0;
.everyonelovesstackoverflowposition:absolute;height:1px;width:1px;opacity:0;top:0;left:0;pointer-events:none;
$begingroup$
I came across a puzzle from a workbook for primary school students who wish to sit in exams for enrolling to selective high schools, which asks about what is the next number in the series.
What is the next number in the series?
21, 21, 23, 20, 5, 25, 31, 24, ?
(A) 3
(B) 10
(C) 17
(D) 86
(Original image)
I've thought many possibilities but none is satisfactory.
What is the next number?
pattern number-sequence
$endgroup$
add a comment
|
$begingroup$
I came across a puzzle from a workbook for primary school students who wish to sit in exams for enrolling to selective high schools, which asks about what is the next number in the series.
What is the next number in the series?
21, 21, 23, 20, 5, 25, 31, 24, ?
(A) 3
(B) 10
(C) 17
(D) 86
(Original image)
I've thought many possibilities but none is satisfactory.
What is the next number?
pattern number-sequence
$endgroup$
15
$begingroup$
I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
$endgroup$
– Charles Hudgins
Sep 30 at 4:09
1
$begingroup$
@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
$endgroup$
– im_so_meta_even_this_acronym
Sep 30 at 4:51
add a comment
|
$begingroup$
I came across a puzzle from a workbook for primary school students who wish to sit in exams for enrolling to selective high schools, which asks about what is the next number in the series.
What is the next number in the series?
21, 21, 23, 20, 5, 25, 31, 24, ?
(A) 3
(B) 10
(C) 17
(D) 86
(Original image)
I've thought many possibilities but none is satisfactory.
What is the next number?
pattern number-sequence
$endgroup$
I came across a puzzle from a workbook for primary school students who wish to sit in exams for enrolling to selective high schools, which asks about what is the next number in the series.
What is the next number in the series?
21, 21, 23, 20, 5, 25, 31, 24, ?
(A) 3
(B) 10
(C) 17
(D) 86
(Original image)
I've thought many possibilities but none is satisfactory.
What is the next number?
pattern number-sequence
pattern number-sequence
edited Sep 30 at 13:37
Andrew T.
1096 bronze badges
1096 bronze badges
asked Sep 29 at 9:48
Michael MayMichael May
7352 silver badges8 bronze badges
7352 silver badges8 bronze badges
15
$begingroup$
I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
$endgroup$
– Charles Hudgins
Sep 30 at 4:09
1
$begingroup$
@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
$endgroup$
– im_so_meta_even_this_acronym
Sep 30 at 4:51
add a comment
|
15
$begingroup$
I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
$endgroup$
– Charles Hudgins
Sep 30 at 4:09
1
$begingroup$
@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
$endgroup$
– im_so_meta_even_this_acronym
Sep 30 at 4:51
15
15
$begingroup$
I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
$endgroup$
– Charles Hudgins
Sep 30 at 4:09
$begingroup$
I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
$endgroup$
– Charles Hudgins
Sep 30 at 4:09
1
1
$begingroup$
@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
$endgroup$
– im_so_meta_even_this_acronym
Sep 30 at 4:51
$begingroup$
@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
$endgroup$
– im_so_meta_even_this_acronym
Sep 30 at 4:51
add a comment
|
3 Answers
3
active
oldest
votes
$begingroup$
I would expect the answer to be
A) 3
Because
If you look at how each term is reached from the last it looks like $times1,+2,-3,div4,times5,+6,-7$ and if we were to continue this it would be $div8$.
$24div8 = 3$
$endgroup$
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
add a comment
|
$begingroup$
I think the answer is
A) 3
My reasoning
21=21*1, 23=21+2, 20=23-3, 5=20/4, 25=5*5, 31=25+6, 24=31-7. Each new term is generated by doing 'something' to the previous term. This something cycles between multiplication, addition, subtraction and division. Also the values used increase by 1. So the next number should be 24/8 = 3. Unfortunately this integer sequence breaks down the next time we need to divide as we have 26/12, which is not integer.
$endgroup$
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
add a comment
|
$begingroup$
3
It is a sequence of addition, subtraction, division and multiplication
$endgroup$
6
$begingroup$
Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
2
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
add a comment
|
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I would expect the answer to be
A) 3
Because
If you look at how each term is reached from the last it looks like $times1,+2,-3,div4,times5,+6,-7$ and if we were to continue this it would be $div8$.
$24div8 = 3$
$endgroup$
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
add a comment
|
$begingroup$
I would expect the answer to be
A) 3
Because
If you look at how each term is reached from the last it looks like $times1,+2,-3,div4,times5,+6,-7$ and if we were to continue this it would be $div8$.
$24div8 = 3$
$endgroup$
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
add a comment
|
$begingroup$
I would expect the answer to be
A) 3
Because
If you look at how each term is reached from the last it looks like $times1,+2,-3,div4,times5,+6,-7$ and if we were to continue this it would be $div8$.
$24div8 = 3$
$endgroup$
I would expect the answer to be
A) 3
Because
If you look at how each term is reached from the last it looks like $times1,+2,-3,div4,times5,+6,-7$ and if we were to continue this it would be $div8$.
$24div8 = 3$
edited Sep 29 at 10:13
answered Sep 29 at 10:06
AdamAdam
2,2371 gold badge7 silver badges36 bronze badges
2,2371 gold badge7 silver badges36 bronze badges
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
add a comment
|
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
6
6
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
$begingroup$
Thank you, Adam. I think that's how the sequence was made.
$endgroup$
– Michael May
Sep 29 at 11:01
add a comment
|
$begingroup$
I think the answer is
A) 3
My reasoning
21=21*1, 23=21+2, 20=23-3, 5=20/4, 25=5*5, 31=25+6, 24=31-7. Each new term is generated by doing 'something' to the previous term. This something cycles between multiplication, addition, subtraction and division. Also the values used increase by 1. So the next number should be 24/8 = 3. Unfortunately this integer sequence breaks down the next time we need to divide as we have 26/12, which is not integer.
$endgroup$
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
add a comment
|
$begingroup$
I think the answer is
A) 3
My reasoning
21=21*1, 23=21+2, 20=23-3, 5=20/4, 25=5*5, 31=25+6, 24=31-7. Each new term is generated by doing 'something' to the previous term. This something cycles between multiplication, addition, subtraction and division. Also the values used increase by 1. So the next number should be 24/8 = 3. Unfortunately this integer sequence breaks down the next time we need to divide as we have 26/12, which is not integer.
$endgroup$
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
add a comment
|
$begingroup$
I think the answer is
A) 3
My reasoning
21=21*1, 23=21+2, 20=23-3, 5=20/4, 25=5*5, 31=25+6, 24=31-7. Each new term is generated by doing 'something' to the previous term. This something cycles between multiplication, addition, subtraction and division. Also the values used increase by 1. So the next number should be 24/8 = 3. Unfortunately this integer sequence breaks down the next time we need to divide as we have 26/12, which is not integer.
$endgroup$
I think the answer is
A) 3
My reasoning
21=21*1, 23=21+2, 20=23-3, 5=20/4, 25=5*5, 31=25+6, 24=31-7. Each new term is generated by doing 'something' to the previous term. This something cycles between multiplication, addition, subtraction and division. Also the values used increase by 1. So the next number should be 24/8 = 3. Unfortunately this integer sequence breaks down the next time we need to divide as we have 26/12, which is not integer.
answered Sep 30 at 2:48
Dmitry KamenetskyDmitry Kamenetsky
5,4589 silver badges51 bronze badges
5,4589 silver badges51 bronze badges
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
add a comment
|
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
4
4
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
$begingroup$
Nobody said that all the elements in the sequence have to be integers.
$endgroup$
– phoog
Sep 30 at 6:48
3
3
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
$begingroup$
An interesting challenge would be to see if changing the starting number would allow you to continue the sequence for longer before getting a non-integer result. I suspect that you couldn't get too high because of that pesky divide step. There might be a proof somewhere that shows that such a sequence would always eventually break...
$endgroup$
– Darrel Hoffman
Sep 30 at 14:32
3
3
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
$begingroup$
@DarrelHoffman I wrote a program to check this. It turns out that we cannot get more than 9 steps before reaching a non-integer value. 9 steps occur when we start from $32n-11$, for any $n geq 1$.
$endgroup$
– Dmitry Kamenetsky
Oct 1 at 0:42
2
2
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
$begingroup$
Could it possibly go for longer by changing the order of operations? There's 24 different ways of mixing them up, might take a while to try them all with a variety of different starting points. If we could somehow get a sequence that doesn't terminate so early, it might be worthy of the OEIS...
$endgroup$
– Darrel Hoffman
Oct 1 at 13:28
2
2
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
$begingroup$
@DarrelHoffman great minds think alike! I already did exactly what you suggested and created an OEIS sequence about it. It is still not approved, but it will be A327962. If you start with 27846 and alternate between /,+,-,* you can make 24 terms before you reach a non-integer.
$endgroup$
– Dmitry Kamenetsky
Oct 2 at 2:15
add a comment
|
$begingroup$
3
It is a sequence of addition, subtraction, division and multiplication
$endgroup$
6
$begingroup$
Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
2
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
add a comment
|
$begingroup$
3
It is a sequence of addition, subtraction, division and multiplication
$endgroup$
6
$begingroup$
Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
2
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
add a comment
|
$begingroup$
3
It is a sequence of addition, subtraction, division and multiplication
$endgroup$
3
It is a sequence of addition, subtraction, division and multiplication
edited Sep 30 at 6:01
trolley813
4,5468 silver badges33 bronze badges
4,5468 silver badges33 bronze badges
answered Sep 30 at 4:44
user62867user62867
19
19
6
$begingroup$
Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
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– Alconja
Sep 30 at 4:59
2
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Also, you should avoid a one-line answer and explain how you came up with that answer.
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– Zoma
Oct 1 at 9:13
add a comment
|
6
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Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
2
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
6
6
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Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
$begingroup$
Welcome to Puzzling. This appears to be correct, however the correct answer has already been posted above.
$endgroup$
– Alconja
Sep 30 at 4:59
2
2
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
$begingroup$
Also, you should avoid a one-line answer and explain how you came up with that answer.
$endgroup$
– Zoma
Oct 1 at 9:13
add a comment
|
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15
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I understand the point of questions like this, but I've noticed that they tend to teach math students that sequences have to follow an obvious pattern. On the contrary, there are approximately 800 distinct, mathematically interesting sequences that feature 1,2,4,8,16 in that order.
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– Charles Hudgins
Sep 30 at 4:09
1
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@CharlesHudgins funny that you mention this given this recent question: puzzling.stackexchange.com/questions/89273/…
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– im_so_meta_even_this_acronym
Sep 30 at 4:51