# A digital clock shows the time from 00:00 to 23:59 as a string of four digits?

1. Aug 22, 2011

### TinyTex

a digital clock shows the time from 00:00 to 23:59 as a string of four digits

1) how many contain for different strings 4 values e.g. 02:43

i got is as 290 dont think its right

since there are
01,02,03,04,05,06,07,08,09,12 = 10
then there are
22,23,24,25,26,27,28,29,32,34,35,36,37,38,39,42,43,45,46,47,48,49,52,53,54,56,57,58,59
= 29

29x10=290

2) How many contain 3 of the same digit

00: 01,02,03,04,05,06,07,08,09,10,20,30,40,50 =14
11: 01,12,13,14,15,16,17,18,19,21,31,41,51 =13
01,02,03,04,05, : 00,00,00,00,00,00,11,22,33,44,55, =10
06,07,09, : 00,00,00 = 3
14+13+10+3= 40?
12

2. Aug 22, 2011

### LCKurtz

Me neither. And you mean "don't". Think of it this way -- how many ways can you pick the first digit? After that is done, how many ways for the second? Then the third? So...

Again, break it into steps. How many ways can you choose the slot for the different digit? How many ways can you choose the digit for that slot? How many ways can you fill the other three slots?

3. Aug 22, 2011

### PeterO

There is also 10, 13,14, ... ,19, 20,21,23,24 as possible openers

Then you need to consider the 3rd digit comes from a smaller set than the 4th digit.

I would be using a tree diagram - at least an imagined one as there are lots of branches.

For the second example I would probably consider, separately, the alternative position of the different digit displayed. And again satisfy thoughts with a tree diagram.