Digital Clock Riddle

[didi0317]

Has anyone figured out the digital clock riddle? I have tried so many variations of numbers.

[didi0317]

Thank you for the answer I found in Discussions.

[shur1kenz]

Originally posted by didi0317:

Thank you for the answer I found in Discussions.

What was it?

[vertigoelectric]

The guide posted provides the answer for this riddle but I'd like to know how it was worked out. There are a number of ways this riddle can be interpreted and none of the ways I tried were successful.

[Declan]

Originally posted by vertigoelectric:

The guide posted provides the answer for this riddle but I'd like to know how it was worked out. There are a number of ways this riddle can be interpreted and none of the ways I tried were successful.

I'm pretty sure they just forgot to count the extra "1" in 11. The puzzle makes sense if you count that extra 1 out.

[mspring]

372 -->

Minutes 1st: 01, 10 --> 19, 21,31,41,51 = 15 times (counting 11 as only 1 occurrence). Multiply this by 24 = 360 times in 24 hours.

Hours 2nd: 01,10 --> 19, 21 = 12 times.

360 + 12 = 372

I agree there are far smarter ways to get a different answer.

[hamsterofdeath]

the definition of "appear" is very vague.
i first counted the number of times the 1 appears like this:
00:01 <- 1
11:11 <- 4
11:12 <- 3

then i just counted the times that contain at least one one, but that wasn't correct either.

[Bananen-Joe]

Just to be complete, I wrote a computer program which counts how often the 1 appears.
There are two possibilites how to count it:
01:11 = one times the 1
OR
01:11 = three times the 1

For the first version I got 900 possible digital clock displays, which are showing at least once the 1 (also 900 times the 1 in 24 hours).
For the second version I got 1164 times the 1 in 24 hours.

The accepted solution 372 is simply wrong.
The correct formula for the first solution is:
matching minutes * not matching hours per day + matching minutes * matching hours per day + not matching minutes per hour * matching hours per day.
So it is:
15 * 12 + 15 * 12 + (60 - 15) * 12 = 900

The second solution is much more complicated to calculate:
We have 60 different minutes and 24 different hours.
The last minute digit can be: 01, 11, 21, 31, 41, 51 (= 6 times of 60)
The first minute digit can be: 10 to 19 (= 10 times of 60)
The last hour digit can be: 01, 11, 21 (= 3 times of 24)
The first hour digit can be: 10 - 19 (= 10 times of 24)
We have 24 * 60 = 1440 different numeric displays per day.

So the formula is:
(10 / 24 + 3 / 24 + 10/60 + 6/60) * 1440 = 1164

The developers simply messed this up... :-/

[vertigoelectric]

Originally posted by Bananen-Joe:

Just to be complete, I wrote a computer program which counts how often the 1 appears.
There are two possibilites how to count it:
01:11 = one times the 1
OR
01:11 = three times the 1

For the first version I got 900 possible digital clock displays, which are showing at least once the 1 (also 900 times the 1 in 24 hours).
For the second version I got 1164 times the 1 in 24 hours.

The accepted solution 372 is simply wrong.
The correct formula for the first solution is:
matching minutes * not matching hours per day + matching minutes * matching hours per day + not matching minutes per hour * matching hours per day.
So it is:
15 * 12 + 15 * 12 + (60 - 15) * 12 = 900

The second solution is much more complicated to calculate:
We have 60 different minutes and 24 different hours.
The last minute digit can be: 01, 11, 21, 31, 41, 51 (= 6 times of 60)
The first minute digit can be: 10 to 19 (= 10 times of 60)
The last hour digit can be: 01, 11, 21 (= 3 times of 24)
The first hour digit can be: 10 - 19 (= 10 times of 24)
We have 24 * 60 = 1440 different numeric displays per day.

So the formula is:
(10 / 24 + 3 / 24 + 10/60 + 6/60) * 1440 = 1164

The developers simply messed this up... :-/

Nice work. I think the devs should fix it.