Pheeb was playing a treasure hunt. She reached her last clue. In the last leg of the hunt, she got a locked diary. She also got a note that said that to unlock the diary, she has to enter a number between 60 and 460, and it is an odd number. The clue also said that the numbers belong to the set: 0, 1, 2, 3, 4, 5. What will be the maximum number of trials that Pheeb has to take to unlock the lock of the diary?
Answers
Given : a number between 60 and 460, and it is an odd number. The clue also said that the numbers belong to the set: 0, 1, 2, 3, 4, 5.
To Find : Maximum possible numbers
Solution:
Number between 60 to 460
Number is odd
numbers belong to the set: 0, 1, 2, 3, 4, 5.
Hence unit digit must be 1 , 3 or 5
100 Digit digit can be 1 , 2 , 3 , 4
Tens Digit can be any of 0, 1, 2, 3, 4, 5.
if repetition of digits is allowed
Then 4 * 6 * 3 = 72 Possible numbers
72 trials required
if repetition of digits not allowed
when 100 Digit is 1 , 3 or 5 - 3 ways then unit digit can be 2 ways
and 10's digit 4 ways
3 * 2 * 4 = 24
when 100 Digit is 2 or 4 - 2 ways then unit digit can be 3 ways
and 10's digit 4 ways
2 * 3 * 4 = 24
Hence 48 trials required
repetition of digits is allowed : 72 trials
repetition of digits not allowed : 48 trials
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