Studying

Number Theory Level 2

Milena began studying when her digital clock showed 20:14, and only stopped when the clock showed the same digits again, for the last time before midnight. How long had she studied?

Notes: To show the same digits means that, if the clock shows 13:15, that clock shows the same digits next at 15:13.

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3 hours and 56 minutes 50 minutes 1 hour and 26 minutes 1 hour

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Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Vaibhav Borale
Jul 27, 2014

Given time is 20:14

Clock will show same digits 3 times before midnight.

That are:- (a) 20:41 (b) 21:04 (c) 21:40

So, "for the last time" points to (c) 21:40

Measuring the time, we get, 1 hr & 26 min.

33 Helpful 0 Interesting 0 Brilliant 1 Confused

nice sum , got clear explanation also

Vignesh Yoganarayanan - 6 years, 10 months ago

what about given in notes.. example 13:15 as 15:13. i took it as two digit number and made mistake.. :-(

Sudhanshu Kumar - 6 years, 10 months ago

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it asked for the same digits, not numbers. so let us remember that we have only ten digits and that is zero to nine. ;]

Elan Joseph Peraren - 6 years, 10 months ago

I MISSED IT UGHHHH

Victor Lai - 6 years, 10 months ago

very nice explanation, I got it right the first time, but still very appreciated for in depth analysis :)

Fritz Legaspi - 6 years, 10 months ago

what about 50 mints? adding 50 mints with 20.14 its becomes 21:04 ..so why not 50 mint is correct?

Salman Khan - 6 years, 10 months ago

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read the question again!! its asked for the last time before midnight

Ribin Babu - 6 years, 10 months ago

Same problem here... a stupid mistake to do.

Bence Mitlasóczki - 6 years, 10 months ago

because at that time, it wasn't the last time the clock showed the same digits before midnight

Laith Diab - 6 years, 10 months ago

20:14 is current time.......it is asking about time with same repeating digits BEFORE MIDNIGHT

VAIBHAV borale - 6 years, 10 months ago

I want a clear explanation for this ques can u explain me

Nivedha Jeyaraman - 6 years, 10 months ago

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Look, given time is 20:14

There are 4 digits here wise '2', '0', '1', '4'

Thus, there are 3 possible ways of rearranging these digits in digital time format (Before midnight as it said).

That are:- (a) 20:41 (b) 21:04 (c) 21:40

Among the above 3 timings the closest one to midnight i.e. 24:00 is (c) 21:40

Calculate the difference between current time 20:14 and last clock with same digits i.e. 21.40, we get the total time Milena studied which is 1hr and 26 min.

VAIBHAV borale - 6 years, 10 months ago

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yeah gud one

Vaibhavi Deshpande - 6 years, 10 months ago

thank yu for ur explanation

Nivedha Jeyaraman - 6 years, 10 months ago
Henrique Ribeiro
Jul 31, 2014

The two options that can be answered by the alternatives, are 50 minutes (21:04) and 1 hour and 26 minutes (21:40). How the question asks the last time, it's 1 h 26 min.

1 Helpful 0 Interesting 0 Brilliant 1 Confused

The biggest digit is 4 but 24:01 or 24:10 is after midnight. So , it must be 1 the second digit. The last time will be when the third digit is the biggest possible. In conclusion, the "last time" is 21:40. We obtain 1 h & 26 min.

0 Helpful 0 Interesting 0 Brilliant 1 Confused

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