Worked solution
Count possible phone numbers before excluding the correct one
A girl wishes to phone a friend but cannot remember the exact number. She knows that it is a five-digit number, that it is even, and that it consists of the digits 2, 3, 4, 5 and 6 in some order. Using this information, find the largest number of different wrong telephone numbers she could try.
[2002/I/17(b)]
CJC · Discussion · Question 2
Answer
71 wrong numbers.
Fill the restricted position first
The final digit has 3 choices: 2, 4 or 6. After fixing it, fill the remaining positions from right to left with 4, 3, 2 and 1 choices. The source boxes therefore read 1, 2, 3, 4, 3 from left to right, with a leftward filling arrow. There are possible numbers.
Remove the one correct number
Exactly one of these possibilities is her friend’s number. In the worst case she tries all the others first: different wrong guesses.
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Common mistakes
The question asks for wrong guesses, so the correct number must be excluded.
Solution notes
All printed asks, working, counting factors and source annotations visually compared and retained. No marks are printed for this question.