Math Problem Statement
Yesterday, I wrote down my friend's phone number. The number I wrote down is six digits, but I remember my friend said that it was the seventh number. I don't know what digit I forgot, nor do I know where the forgotten digit is. How many phone numbers should I forget? I should try to make sure I got the right number??
Solution
To determine how many possible seven-digit phone numbers could result from your six-digit number with one missing digit, we need to consider that:
- There are 7 positions where the missing digit could be inserted (before, between, or after any of the six digits).
- Each of those 7 positions could contain any of the 10 digits (0–9).
Thus, the total number of possible phone numbers can be calculated by multiplying the number of positions by the number of possible digits:
Therefore, you would need to try 70 different phone numbers to ensure you have the correct one.
Would you like more details or have any other questions?
Here are 5 related questions to expand on this:
- What if the phone number had more or fewer digits?
- How many possibilities would there be if you forgot two digits instead of one?
- How can this concept be applied in cryptography or data recovery?
- What methods could you use to narrow down the possibilities?
- How does this problem relate to permutation or combination theory?
Tip: In problems like this, identifying positions for insertion or missing items often involves basic combinatorics.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Basic Arithmetic
Formulas
Total possibilities = Number of positions × Number of possible digits
7 × 10 = 70
Theorems
Basic principles of counting in combinatorics
Suitable Grade Level
Grades 6-8
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