75
We'll just apply a bit of science assuming they were born in same year as well:
68
A very simple solution, taking
is to
A better solution takes only
How?
61
Since a stopped clock already agrees with a correctly running clock twice per day,
So the answer (that requires the smallest clock hand speed) is
Since the answer must be symmetrical (as long as the difference in speeds remains the same, it doesn't matter if our clock is getting ahead or behind the correctly running one), we can get the other answer by ...
58
Hint: You can light both sides of one rope. Solution:
56
50
It is
47
They were born on
46
Apply some other bit of science, assuming they were born at the same time,
45
Foo is older than Bar, but celebrates his birthday the day after Bar because one of the following happened:
37
Is it lateral-thinking?
32
Similar to Daniel's answer but a slight variation:
30
Suppose we have an accurate clock and the fast clock, and that they start off showing the same time.
Here is an alternative method:
29
The day is
Reasoning:
Classic Mind Puzzle :) My fav <3
28
The answer is simply:
I have heard this one before but I don't remember where, maybe the movie you mentioned.
26
Let us denote the time by AB:CD:EF, where AB is between 00 and 23, CD and EF are each between 00 and 59, and of course A=F, B=E, C=D.
The middle two digits
Since C=D and CD ranges from 00 to 59, there are six possibilities: 00, 11, 22, 33, 44, 55.
The outer four digits
The first two digits (AB) range from 00 to 23. How many of these possibilities give ...
24
At noon, all three hands are at $0$ degrees from each other.
Let's say the Moment of Truth is after the hour hand has moved around $x$ degrees. In that time, the minute hand moves $12x$ degrees and the second hand moves $720x$ degrees. So we want $x, 12x\pmod{360},$ $720x \pmod {360}$ to be separated by $120$ from each other.
From the minute and second ...
24
22 minutes with lateral thinking (though the accepted answer is better)
23
Because they are...
And they were born...
And...
23
Alternative method:
The answer to how fast the clock must go:
22
First produce 48 by putting the traces up/down/up/down/up in the freezer. Then use 18 of the ice cubes and put them in the corners of the botton 6 trays, produce 66 more ice cubes. Do this 2 more times and get 246 in total.
Possibly could make 264 if you can balance using 2 cubes only.
21
Would it be because:
20
You and your twin were born:
20
It is currently
and the older brother is
How I figured this out:
20
Logic behind the answer:
So, without really looking at anything else, my initial guess is:
resulting in:
Note:
Edit:
19
Ok I will present a solution.
For convenience, I will number the ropes in the order of their burning.
STEP ONE
STEP TWO
STEP THREE
FINAL STEP
I have successfully measured 1hour 8 minutes or 68 minutes
19
Number of qualifying times:
Probability:
18
The date of the accident is
Explanation
17
There are
Because
17
The clockface is divided into $60$ segments.
Only top voted, non community-wiki answers of a minimum length are eligible