Codes with no confusion

  • Thread starter Robert Houdart
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In summary, there are 81 possible codes that can be formed by selecting two distinct digits from 0-9, where the first digit cannot be zero. However, out of these 81 codes, 12 of them may cause confusion when read upside down, such as 91 appearing as 16. These numbers are 1, 6, 8, and 9, and the pairs 16, 61, 18, 81, 19, 91, 68, 86, 89, and 98. Therefore, the total number of codes for which no confusion can arise is 81-12=69.
  • #1
Robert Houdart
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Homework Statement



An intelligence agency forms a code of two distinct digits selected from 0, 1 , 2…, 9, such that the first digit of the code is nonzero. The code, handwritten on a slip, can, however, potentially create confusion when read upside down - for example; the code 91 may appear as 16. How many codes are there for which no such confusion can arise?
2. The attempt at a solution
This is the methodology I used:
Since the first digit cannot be zero, therefore it can be chosen in 9 ways while no restriction occurs on the second number, therefore it can be chosen in 10 ways.Thus, the total number of ways is 10*9=90...

Since 1,6,8,9 can create confusion, therefore there exist 12 such numbers which will create confusion. However the pair 69 and 96 do not come under this category.
 
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  • #2
Mod note: This post was a response in a separate cross-posted thread.
Since the first digit cannot be zero, therefore it can be chosen in 9 ways while no restriction occurs on the second number,...
... there are not nine possible choices for the 1st digit. Which other digits are excluded?
1,6,8,9 can create confusion,
... there you go ... so how many digits may be chosen from for the 1st number and how many for the second number?
the pair 69 and 96 do not come under this category.
... good thinking - these are numbers that are the same upside down ... are there others? i.e. what about 11?
 
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  • #3
Mod note: This post was a response in a separate cross-posted thread.Ok, I think I got it. Since they are distinct numbers, the first digit can be chosen in 9 ways (except 0) while the second can also be chosen in 9 ways, making it 81 numbers instead of 90.. So am I right this time?
 
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  • #4
Robert Houdart said:
Since 1,6,8,9 can create confusion, therefore there exist 12 such numbers which will create confusion.
Are you sure it's only 12? Spell out your logic.
 
  • #5
well , considering 69 and 96 total number pertains to 10
 
  • #6
Robert Houdart said:
well , considering 69 and 96 total number pertains to 10
No, I mean I think you missed a few before discounting those two. I think it will help if you write out in detail your reasoning for the count of 12.
 
  • #7
(16,61) (18,81) (19,91) (68 ,86) (89, 98) i think these are all (actually total number of numbers were 81 instead of 90 (digits must be distinct)
 
  • #8
Robert Houdart said:
(actually total number of numbers were 81 instead of 90 (digits must be distinct)
Ah, that explains it. I missed that condition.
So now I agree with your answers.
 

1. What is a "code with no confusion"?

A "code with no confusion" refers to a system of symbols or signals used to represent information without any ambiguity or uncertainty. This means that each symbol or signal has a clear and distinct meaning, leaving no room for confusion or misinterpretation.

2. How are codes with no confusion used?

Codes with no confusion can be used in various fields such as computer programming, cryptography, and communication systems. They are also used in everyday life, for example, in barcodes, traffic signals, and medical alert symbols.

3. What are the advantages of using codes with no confusion?

The main advantage of using codes with no confusion is that they allow for efficient and accurate communication of information. They also reduce the chances of errors and misunderstandings, which can save time and resources.

4. Are there any downsides to using codes with no confusion?

The downside of using codes with no confusion is that they can be more complex and require a certain level of understanding to interpret. This means that they may not be suitable for all situations or audiences.

5. How can I create a code with no confusion?

To create a code with no confusion, you need to carefully select and define each symbol or signal to represent a specific meaning. The code should also be tested and refined to ensure that it is easily understandable and error-proof.

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