### Brain Teasers

# Clock Ticks

A man had a clock with an hour hand and a minute hand of the same length and indistinguishable. If the clock was set going at noon, what would be the first time that it would be impossible, by reason of the similarity of the hands, to be sure of the correct time?

In grappling with this little problem, you may assume that it is possible to indicate fractions of a second. On this assumption, an exact answer can be given.

In grappling with this little problem, you may assume that it is possible to indicate fractions of a second. On this assumption, an exact answer can be given.

### Answer

The first time would be 5 and 5\143 minutes past 12, which might also indicate 60\143 minutes past 1. Expressed slightly less accurately, 5 minutes past 12 and about half a minute past 1.Hide Answer Show Answer

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## Comments

Ummmmm...what's the word I'm looking for?

i agree tissue, this makes no sense.

Sure it makes sense. If you have a clock where the minute and hour hand are the same length, only certain times are distinguishable using only the clock. For example, 12:30 and 60 would NOT be distinguisable because either time could be the other, but 125 would have to 125 based on the position of the hands. Besides, you two are editors, so shame on you, lol.

HUH????!!!!!!!!!

I think it is much better when a solution is explained rather than just an answer given, especially when some answers are in fact wrong.

This one is correct.

Consider a clock with at noon.

The big hand is at 6x deg at x min past 12

The little hand is at x/2 deg at x min past 12

Now the answer is obviously about 5 past 12 when it might also look close to 1 o'clock.

Consider a clock at 10 hands are 30 deg apart

The little hand is at 30 + y/2 at y min after 1

The big hand is at 6y y min after 1

If the hands now become confused (big = little etc)

6x = 30 + y/2 }

x/2 = 6y }

sub 2 in 1 6x = 30 + x/24

144x = 720 + x

143x = 720

x = 5 and 5/143 (y = 60/143)

So at 5 and 5/143 min past 12 the hands may be swapped and it could be 60/143 min after 1.

Excellent teaser BTW

This one is correct.

Consider a clock with at noon.

The big hand is at 6x deg at x min past 12

The little hand is at x/2 deg at x min past 12

Now the answer is obviously about 5 past 12 when it might also look close to 1 o'clock.

Consider a clock at 10 hands are 30 deg apart

The little hand is at 30 + y/2 at y min after 1

The big hand is at 6y y min after 1

If the hands now become confused (big = little etc)

6x = 30 + y/2 }

x/2 = 6y }

sub 2 in 1 6x = 30 + x/24

144x = 720 + x

143x = 720

x = 5 and 5/143 (y = 60/143)

So at 5 and 5/143 min past 12 the hands may be swapped and it could be 60/143 min after 1.

Excellent teaser BTW

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