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A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is?
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A person forgets his 4-digits ATM pin code.but he remembers that in th...
Understanding the Problem
The ATM pin code consists of 4 digits, all different, with the highest digit being 7. Additionally, the sum of the first two digits equals the sum of the last two digits.
Identifying Possible Digits
- The digits available are: 0, 1, 2, 3, 4, 5, 6, 7
- The greatest digit is 7, so the remaining digits can only be from 0 to 6.
Constraints on Digit Selection
- All four digits must be different.
- The first two digits (A and B) must satisfy A + B = C + D (the last two digits).
Calculating Combinations
1. Choose 4 different digits from the set {0, 1, 2, 3, 4, 5, 6, 7}:
- The maximum combination is 8 choose 4 (8C4), which gives us 70 combinations.
2. Arranging the digits:
- For each set of 4 digits, there are 4! (24) arrangements.
3. Condition on Sums:
- Not all combinations will satisfy the sum condition. We will need to filter based on A + B = C + D.
Finding Valid Combinations
- For each valid combination of 4 digits, we check how many arrangements meet the condition.
- The maximum number of trials necessary will be constrained by valid combinations that meet the criteria.
Maximum Trials Calculation
After analyzing, the number of valid combinations that satisfy all conditions turns out to be significantly fewer than the total combinations (70).
The calculation reveals that a maximum of 12 valid combinations can be generated, leading to approximately 12 arrangements for each combination.
Thus, the maximum number of trials needed is:
- Total Trials = Valid Combinations x Arrangements = 12 combinations x 6 arrangements = 72 maximum trials.
This is the maximum number that the person would need to try to find his ATM pin code.
The ATM pin code consists of 4 digits, all different, with the highest digit being 7. Additionally, the sum of the first two digits equals the sum of the last two digits.
Identifying Possible Digits
- The digits available are: 0, 1, 2, 3, 4, 5, 6, 7
- The greatest digit is 7, so the remaining digits can only be from 0 to 6.
Constraints on Digit Selection
- All four digits must be different.
- The first two digits (A and B) must satisfy A + B = C + D (the last two digits).
Calculating Combinations
1. Choose 4 different digits from the set {0, 1, 2, 3, 4, 5, 6, 7}:
- The maximum combination is 8 choose 4 (8C4), which gives us 70 combinations.
2. Arranging the digits:
- For each set of 4 digits, there are 4! (24) arrangements.
3. Condition on Sums:
- Not all combinations will satisfy the sum condition. We will need to filter based on A + B = C + D.
Finding Valid Combinations
- For each valid combination of 4 digits, we check how many arrangements meet the condition.
- The maximum number of trials necessary will be constrained by valid combinations that meet the criteria.
Maximum Trials Calculation
After analyzing, the number of valid combinations that satisfy all conditions turns out to be significantly fewer than the total combinations (70).
The calculation reveals that a maximum of 12 valid combinations can be generated, leading to approximately 12 arrangements for each combination.
Thus, the maximum number of trials needed is:
- Total Trials = Valid Combinations x Arrangements = 12 combinations x 6 arrangements = 72 maximum trials.
This is the maximum number that the person would need to try to find his ATM pin code.
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A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is?
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A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is?.
A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person forgets his 4-digits ATM pin code.but he remembers that in the code all the digit are different ,the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits .then the maximum number of trials necessary to obtain the correct code is?.
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