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Saumyojit

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An intelligence agency forms a code of two distinct digits selected from 0,1,2,3,……9 such that the first digit of the code is non-zero. The code handwritten on a slip, can however potentially create confusion when read upside down i.e, the code 91 may appear as 16.How many codes are there for which no confusion can arise.​


According to my knowledge , 6 and 9 creates the confusion of all 10 digits.
No of two distinct digit no = 81 nos

fixing 9 in tens place (i) _9_ _9ways_ (0-8)
fixing 9 in units place (ii) _8ways_ (1-8) _9_
fixing 6 in ten's place (iii) _6_ _8ways_ (0-8) (No 6!)
fixing 6 in units place (iv) _7ways_ (1-8) (No 6!) _6_

Adding these gives me 32 nos .
81 - 32 = 49 nos . But this is not the answer !
 
Saumyojit said:

An intelligence agency forms a code of two distinct digits selected from 0,1,2,3,……9 such that the first digit of the code is non-zero. The code handwritten on a slip, can however potentially create confusion when read upside down i.e, the code 91 may appear as 16.How many codes are there for which no confusion can arise.​


According to my knowledge , 6 and 9 creates the confusion of all 10 digits.
No of two distinct digit no = 81 nos

fixing 9 in tens place (i) _9_ _9ways_ (0-8)
fixing 9 in units place (ii) _8ways_ (1-8) _9_
fixing 6 in ten's place (iii) _6_ _8ways_ (0-8) (No 6!)
fixing 6 in units place (iv) _7ways_ (1-8) (No 6!) _6_

Adding these gives me 32 nos .
81 - 32 = 49 nos . But this is not the answer !
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I think what is considered to cause confusion may be more subtle than you think (and possibly more than they think -- I disagree with the answer given by a source I found for the problem!). Have you thought about whether 1 and 8 can cause trouble? Can 6 or 9 cause trouble when combined with other digits?

Try actually listing your 32 such numbers, and then think about whether they actually cause confusion, and whether anything else might. Please do this and show your list!

(What you've written is hard to follow; maybe if you used underlines instead of putting underscore characters around a digit, like " 9 , (0-8) " rather than "_9_ _9ways_ (0-8)", it would be easier.)
 
69, 96 ,18, 81, 61,68,91,98,16,19,86,89
ANswer is coming 71 . (81-12 )

WHat about zero ? will it not be there as it produces a single no when read upside down . (10 -> 01) ??

But there are two codes 69 and 96 which look the same even while reading upside down
SO these will not be counted right. So it will 71 .
 
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Saumyojit said:
90, 91,92,93,94,95,96,97,98,99.
19,29,39,49,59,69,79,89
16,26,36,46,56, 76,86
61,62,63,64,65,67,68.
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These are supposed to be the numbers that do cause confusion, right? But only a few of these do (e.g. 91 becomes 16); most don't. This shows that you are thinking incorrectly.

Saumyojit said:
But what do [1 and 8] represent when read upside down i dont find any no
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When they are written upside-down by a typical American, they remain 1 and 8. But I know that many people (perhaps including India?) write 1 very differently; this is one problem with the problem! Where I've seen the answer explained, they assume 1 becomes 1.

Saumyojit said:
69, 96 ,18, 81, 61,68,91,98,16,19,86,89
ANswer is coming 71 . (81-12 )

WHat about zero ? will it not be there as it produces a single no when read upside down . (10 -> 01) ??

But there are two codes 69 and 96 which look the same even while reading upside down
SO these will not be counted right. So it will 71 .
Click to expand...
What caused you to change your mind? Did you see someone else's answer? You appear now to be taking 1 as I did, and you are no longer using irreversible digits.

However, 81 - 12 = 69, not 71! Apparently you meant to say 69, but confused yourself with the answer you saw.

And as you say, 69 and 96 should not be included. But what about 66 and 99? So the answer really is 69. The source I found that gives an answer says 71; they are wrong. They didn't list the numbers, which is really needed in order to be sure you are thinking correctly.

The reason 10 and 01 is not included is that 01 is not allowed because it starts with 0, so if you saw it you would know it is upside-down.

So the correct list of confusable numbers is 16, 18, 19, 61, 66, 68, 81, 86, 89, 91, 98, 99.

The problem, like many you ask about, is not well-written. Yet this appears to be an actual past test question. Is that true?
 
Dr.Peterson said:
These are supposed to be the numbers that do cause confusion, right? But only a few of these do (e.g. 91 becomes 16); most don't. This shows that you are thinking incorrectly.


When they are written upside-down by a typical American, they remain 1 and 8. But I know that many people (perhaps including India?) write 1 very differently; this is one problem with the problem! Where I've seen the answer explained, they assume 1 becomes 1.


What caused you to change your mind? Did you see someone else's answer? You appear now to be taking 1 as I did, and you are no longer using irreversible digits.

However, 81 - 12 = 69, not 71! Apparently you meant to say 69, but confused yourself with the answer you saw.

And as you say, 69 and 96 should not be included. But what about 66 and 99? So the answer really is 69. The source I found that gives an answer says 71; they are wrong. They didn't list the numbers, which is really needed in order to be sure you are thinking correctly.

The reason 10 and 01 is not included is that 01 is not allowed because it starts with 0, so if you saw it you would know it is upside-down.

So the correct list of confusable numbers is 16, 18, 19, 61, 66, 68, 81, 86, 89, 91, 98, 99.

The problem, like many you ask about, is not well-written. Yet this appears to be an actual past test question. Is that true?
Click to expand...
66 and 99 cannot happen only as disitinct digits are to be counted
 
Saumyojit said:
66 and 99 cannot happen only as distinct digits are to be counted
Click to expand...
Yes, I missed that.

But I need to ask you: Do you write 1 so that it is the same upside down, or not? Even if you do (and everyone in your country does), this is not a good problem to use internationally.
 
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