The answer seems to depend upon one's penmanship. Or, alternately, the font.
On a seven-segment display like a calculator's, an upside down 6 becomes a 9 and 5 and 2 remain what they were. I've seen some people's hand-written 6's and 9's do that, but nobody's 5's and 2's.
I think the zero is the only one that's universally the same upside down or not. And I'll concede on the eight and the one.
So, if the font were specified in the question, one could find a defensible answer, but otherwise, "it depends."
So, not only is it not math, but there's also more than one correct answer.
This is ridiculous as extra credit for math but it could be a fun class discussion about using logical reasoning and figuring out what the implied assumptions are when confronted with an unexpected question.
Since the number is between 1000 and 2000 the first digit has to be 1 which means the last digit has to be 1. So the question reduces to how many two digit interior sequences are the same when you turn them upside down. And that, of course, gets into the font assumption.
Typically 00, 11, and 88. (Although one could argue about the 1.) Possibly 69 and 96. I'm not sure about 22 and 55. They are the same upside down on my calculator.
This was a multiple choice question. The possible answers were 3, 4, 5 or 6.
We're still not sure what the actual 5 answers are, or what "upside down" means (my mathematically-inclined son first thought they meant a pallindrome).
1001? 1111? 1881? 1331? 1551? (nah, a 5 turns into a 2 if you turn it upside down). What about 1181? 1811? 1081? 1311?
Upside down. Right. I guess you at least have to include the following, don't you?
1001, 1011, 1101, 1111
How could you get just one more other than that?
And remember: we know in advance the answer is 5. How is my kid supposed to do a multiple choice problem like this?
That's the real problem. So many problems like this, uninterpretable, and most definitely not math, being passed off as math.
Bet you folks that are done with school for this year are happy to be putting some distance between yourselves this craziness!
However, it is a fact that if you write 1011 on a piece of paper, leave the paper flat on the table or desk, and rotate the paper so what was the top is now the bottom (which is how I interpret upside down), it reads 1101 which is not the same. You can check this by trying it.
Susan...I was thinking the same thing about it being fun as a classroom discussion. As it is, it's mean and unfair. It's not properly defined and I could see myself as a kid just disolving into tears over it. Even now I was wondering do they mean reflective symmetry with the line below the number or a horizontal 180 degree turn? And, like everyone's pointing out, font matters.
The question invites further questions but cheats.
It's like asking, "Why do you like the colour red?" and having to answer yes or no.
Strobogrammatic numbers! Well now the puzzle is solved. Here they are, then, and they number five:
1001, 1111, 1691, 1881, 1961
Silly me. The take on it that I had was to draw a line under the number, then swivel it along that axis so they would be "upside down"--the first number would still be the first number (only upside down). I didn't think of taking the whole paper and turning the thing upside down (which reverses the order). So there is a bit of the sense of a pallindrome in it, I guess (rather than the mirror)..oh my, this is just getting very confusing.
I guess I should have looked up the mathematical meaning of "upside down."
This is a quote from the Wikipedia article on strobogrammatic numbers. (Thanks david!)
"Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not."
The article makes a point we all missed: it depends on what base you think the number is in! We all just assumed base 10. Could actually have been anything from 3 on up.
Our discussion here underlines why the question is not appropriate for a math exam. It is wrong for students to get the impression that math is a matter of opinion or even fonts.
Only 5?
ReplyDeleteThe answer seems to depend upon one's penmanship. Or, alternately, the font.
ReplyDeleteOn a seven-segment display like a calculator's, an upside down 6 becomes a 9 and 5 and 2 remain what they were. I've seen some people's hand-written 6's and 9's do that, but nobody's 5's and 2's.
I think the zero is the only one that's universally the same upside down or not. And I'll concede on the eight and the one.
So, if the font were specified in the question, one could find a defensible answer, but otherwise, "it depends."
So, not only is it not math, but there's also more than one correct answer.
Crazy.
This is ridiculous as extra credit for math but it could be a fun class discussion about using logical reasoning and figuring out what the implied assumptions are when confronted with an unexpected question.
ReplyDeleteSince the number is between 1000 and 2000 the first digit has to be 1 which means the last digit has to be 1. So the question reduces to how many two digit interior sequences are the same when you turn them upside down. And that, of course, gets into the font assumption.
Typically 00, 11, and 88. (Although one could argue about the 1.) Possibly 69 and 96. I'm not sure about 22 and 55. They are the same upside down on my calculator.
This was a multiple choice question. The possible answers were 3, 4, 5 or 6.
ReplyDeleteWe're still not sure what the actual 5 answers are, or what "upside down" means (my mathematically-inclined son first thought they meant a pallindrome).
1001? 1111? 1881? 1331? 1551? (nah, a 5 turns into a 2 if you turn it upside down). What about 1181? 1811? 1081? 1311?
Upside down. Right. I guess you at least have to include the following, don't you?
1001, 1011, 1101, 1111
How could you get just one more other than that?
And remember: we know in advance the answer is 5. How is my kid supposed to do a multiple choice problem like this?
That's the real problem. So many problems like this, uninterpretable, and most definitely not math, being passed off as math.
Bet you folks that are done with school for this year are happy to be putting some distance between yourselves this craziness!
I agree this is crazy under the circumstances.
ReplyDeleteHowever, it is a fact that if you write 1011 on a piece of paper, leave the paper flat on the table or desk, and rotate the paper so what was the top is now the bottom (which is how I interpret upside down), it reads 1101 which is not the same. You can check this by trying it.
Susan...I was thinking the same thing about it being fun as a classroom discussion. As it is, it's mean and unfair. It's not properly defined and I could see myself as a kid just disolving into tears over it. Even now I was wondering do they mean reflective symmetry with the line below the number or a horizontal 180 degree turn? And, like everyone's pointing out, font matters.
ReplyDeleteThe question invites further questions but cheats.
It's like asking, "Why do you like the colour red?" and having to answer yes or no.
These are called strobogrammatic numbers, for what it's worth.
ReplyDeleteWhat an idiotic question.
ReplyDeleteThey must all be of the form
1**1, where the ones are written in a font that is not present on this blog. because as it is, the answer is 0.
Assuming they used a calculator font, sans serif, old Liquid Crystal display:
1001 works
1111 works
1251 works
1521 works
1881 works
1691 works
1961 works
and that's more than 5. how could you possibly know that you're supposed to use the 6/9 but not the 5/2?
"Upside down," as Dawn says, is ambiguous. For a calculator, it means face down.
ReplyDeleteThe idiot who wrote this question probably thinks a mirror reverses right and left.
(Not unless you believe it reverses up and down. A mirror reflects front and back.)
>>How many numbers between 1000 and 2000 are the same when you turn them upside down?<<
ReplyDeleteI would have been so bad at this. I immediately thought "all of them." Because, ya' know, they're just upside down, not different.
Strobogrammatic numbers! Well now the puzzle is solved. Here they are, then, and they number five:
ReplyDelete1001, 1111, 1691, 1881, 1961
Silly me. The take on it that I had was to draw a line under the number, then swivel it along that axis so they would be "upside down"--the first number would still be the first number (only upside down). I didn't think of taking the whole paper and turning the thing upside down (which reverses the order). So there is a bit of the sense of a pallindrome in it, I guess (rather than the mirror)..oh my, this is just getting very confusing.
I guess I should have looked up the mathematical meaning of "upside down."
There is an official 4X4 transformation for "upside down"?
ReplyDeleteThis is a quote from the Wikipedia article on strobogrammatic numbers. (Thanks david!)
ReplyDelete"Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not."
The article makes a point we all missed: it depends on what base you think the number is in! We all just assumed base 10. Could actually have been anything from 3 on up.
Our discussion here underlines why the question is not appropriate for a math exam. It is wrong for students to get the impression that math is a matter of opinion or even fonts.
Great comment Steve!
its 6 in total as-1001 1010,1011,1100,1101 & 1111.
ReplyDelete