A multiple-choice quiz
by gentlegiant17.
Estimated time: 23 mins.

Quiz Answer Key and Fun Facts

Answer:
**11**

My watch has 5 LEDs for showing hours: 23 lies between 16 (10000 in binary) and 32 (100000 in binary).

It has 6 LEDs for showing minutes: 59 lies between 32 (100000 in binary) and 64 (1000000 in binary).

Thus, 11 LEDs in total are required.

My watch has 5 LEDs for showing hours: 23 lies between 16 (10000 in binary) and 32 (100000 in binary).

It has 6 LEDs for showing minutes: 59 lies between 32 (100000 in binary) and 64 (1000000 in binary).

Thus, 11 LEDs in total are required.

Answer:
**10:42**

Below, "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

You don't want two adjacent O's in your correct answer.

10:42 looks like this:

XOXOX

OXOXOX

10:43 looks like this:

XOXOX

OXOXOO

11:42 looks like this:

XOXOO

OXOXOX

11:43 looks like this:

XOXOO

OXOXOO

Below, "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

You don't want two adjacent O's in your correct answer.

10:42 looks like this:

XOXOX

OXOXOX

10:43 looks like this:

XOXOX

OXOXOO

11:42 looks like this:

XOXOO

OXOXOX

11:43 looks like this:

XOXOO

OXOXOO

Answer:
**15:47**

Again, "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

07:27 (7 LEDs on):

XXOOO

XOOXOO

12:09 (4 LEDs on):

XOOXX

XXOXXO

15:47 (9 LEDs on):

XOOOO

OXOOOO

19:43 (7 LEDs on):

OXXOO

OXOXOO

Again, "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

07:27 (7 LEDs on):

XXOOO

XOOXOO

12:09 (4 LEDs on):

XOOXX

XXOXXO

15:47 (9 LEDs on):

XOOOO

OXOOOO

19:43 (7 LEDs on):

OXXOO

OXOXOO

Answer:
**9**

The watch can never have all of its hour LEDs on (since 11111 binary is 31 decimal and there is no such hour of the day).

The watch can never have all of its minute LEDs on (since 111111 binary is 63 decimal and there is no such minute of the hour).

There is a number of times during the day where 4 hour LEDs and 5 minute LEDs are on, yielding a maximum total of 9 lit LEDs (hmmmm... can you tell how many?).

The watch can never have all of its hour LEDs on (since 11111 binary is 31 decimal and there is no such hour of the day).

The watch can never have all of its minute LEDs on (since 111111 binary is 63 decimal and there is no such minute of the hour).

There is a number of times during the day where 4 hour LEDs and 5 minute LEDs are on, yielding a maximum total of 9 lit LEDs (hmmmm... can you tell how many?).

Answer:
**224**

The leftmost hour LED is ON at all hours between 16 and 23 (8 in total).

The leftmost minute LED is ON at all minutes between 32 and 59 (28 in total).

Thus, both these LEDs are ON 224 times a day (8*28=224).

The leftmost hour LED is ON at all hours between 16 and 23 (8 in total).

The leftmost minute LED is ON at all minutes between 32 and 59 (28 in total).

Thus, both these LEDs are ON 224 times a day (8*28=224).

Answer:
**9**

Yes, there is an occasion where the number of lit LEDs decreases from its maximum value of 9 to its minimum value of 0 - the passage from 23:59 to midnight.

Yes, there is an occasion where the number of lit LEDs decreases from its maximum value of 9 to its minimum value of 0 - the passage from 23:59 to midnight.

Answer:
**The leftmost hour LED**

The good old leftmost hour LED shifts between states only twice daily: OFF to ON at 16:00 and ON to OFF at 00:00. It is by far the least used LED in my watch.

The good old leftmost hour LED shifts between states only twice daily: OFF to ON at 16:00 and ON to OFF at 00:00. It is by far the least used LED in my watch.

Answer:
**17:33 **

The binary representation of 17 is 10001.

The binary representation of 33 is 100001.

Thus, at 17:33 the LED scheme of my watch is the desired one:

OXXXO

OXXXXO

Where "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

The binary representation of 17 is 10001.

The binary representation of 33 is 100001.

Thus, at 17:33 the LED scheme of my watch is the desired one:

OXXXO

OXXXXO

Where "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

Answer:
**03:31 **

Since it is impossible for all the 6 minute LEDs to be simultaneously on, you are looking for the earliest time where 2 hour LEDs and 5 minute LEDs are on. The meaning of "earliest" is that these LEDs should be justified to the right.

Representing the hour 03:31, here is the LED scheme in question:

XXXOO

XOOOOO

Where "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

Since it is impossible for all the 6 minute LEDs to be simultaneously on, you are looking for the earliest time where 2 hour LEDs and 5 minute LEDs are on. The meaning of "earliest" is that these LEDs should be justified to the right.

Representing the hour 03:31, here is the LED scheme in question:

XXXOO

XOOOOO

Where "X" signifies a LED which is OFF and "O" signifies a LED which is ON.

Answer:
**156**

This one requires a bit of thought and flexibility which will enable you to consider the combinatorics along with the algebra of the watch.

A plain combinatorical calculation of choosing 3 of 11 LEDs will give an answer of 165 (11!/3!*8!). However, this is not the correct answer (which is why I hinted you that I am looking for an even number). Consider the 9 combinations where the 2 leftmost hour LEDs are on - all of them are illegal as they produce an hour of the day larger than 23 (in other words, 11000 binary is 24 decimal).

Thus, the correct answer is 156 (165 combinations minus 9 illegal ones).

This one requires a bit of thought and flexibility which will enable you to consider the combinatorics along with the algebra of the watch.

A plain combinatorical calculation of choosing 3 of 11 LEDs will give an answer of 165 (11!/3!*8!). However, this is not the correct answer (which is why I hinted you that I am looking for an even number). Consider the 9 combinations where the 2 leftmost hour LEDs are on - all of them are illegal as they produce an hour of the day larger than 23 (in other words, 11000 binary is 24 decimal).

Thus, the correct answer is 156 (165 combinations minus 9 illegal ones).

This quiz was reviewed by FunTrivia editor crisw before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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