FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!  # The Binary Watch Trivia Quiz

### Browsing through a duty-free brochure on a recent flight, I spotted an ad for a binary watch. While it was a bit expensive, can you afford to refuse a free quiz?

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

Author
Time
23 mins
Type
Multiple Choice
Quiz #
306,815
Updated
Dec 03 21
# Qns
10
Difficulty
Difficult
Avg Score
4 / 10
Plays
2470
Awards
Top 5% quiz!
Question 1 of 10
1. My binary watch has two rows of LEDs (Light Emitting Diodes).
On its top row, a certain number of LEDs for telling hours.
On its bottom row, a certain numbers of LEDs for telling minutes.

For example, when displaying the hour 03:07, 5 LEDs in total are turned ON:
The 2 rightmost ones of the hour row (as the binary representation of 3 is 11) plus the 3 rightmost ones of the minute row (as the binary representation of 7 is 111).

My watch does not have an AM/PM indicator so please consider hours to be between 0 and 23. Minutes are between 0 and 59. This version of the watch does NOT tell seconds.

In order to be able to display all times between 00:00 and 23:59, how many LEDs in total does my watch have?

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Question 2 of 10
2. In which of the following times of the day NO two adjacent LEDs are turned ON (i.e. adjacent in a given row)? Hint

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Question 3 of 10
3. In which of the following times of the day is the largest number of LEDs turned ON? Hint

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Question 4 of 10
4. What is the maximum number of LEDs in my watch which can be turned ON at a given time of the day?

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Question 5 of 10
5. The leftmost hour and the leftmost minute LEDs are BOTH turned ON.

How many times a day does this happen?

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Question 6 of 10
6. As a single minute passes, what is the maximum number of LEDs which can switch from ON to OFF?

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Question 7 of 10
7. Assuming that the only factor which determines the lifetime of a LED in my watch is the number of times it shifts between ON and OFF states and that all LEDs were installed at the same time, which is the LED that will last the longest time? Hint

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Question 8 of 10
8. What time is it when ONLY the 4 external LEDs in my watch are turned ON (i.e. leftmost and rightmost hour LEDs, leftmost and rightmost minute LEDs)?

Answer: (a time of the day in HH:MM format, e.g. 03:07)

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Question 9 of 10
9. Which is the earliest time of the day when 7 LEDs in total are turned ON?

Answer: (a time of the day in HH:MM format, e.g. 03:07)

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Question 10 of 10
10. This last question may look short and sweet, but be warned not to lose yourself when performing the calculation - it's tricky.

How many times a day exactly 3 LEDs in my watch are turned ON?

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Quiz Answer Key and Fun Facts
1. My binary watch has two rows of LEDs (Light Emitting Diodes). On its top row, a certain number of LEDs for telling hours. On its bottom row, a certain numbers of LEDs for telling minutes. For example, when displaying the hour 03:07, 5 LEDs in total are turned ON: The 2 rightmost ones of the hour row (as the binary representation of 3 is 11) plus the 3 rightmost ones of the minute row (as the binary representation of 7 is 111). My watch does not have an AM/PM indicator so please consider hours to be between 0 and 23. Minutes are between 0 and 59. This version of the watch does NOT tell seconds. In order to be able to display all times between 00:00 and 23:59, how many LEDs in total does my watch have?

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.
2. In which of the following times of the day NO two adjacent LEDs are turned ON (i.e. adjacent in a given row)?

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

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
3. In which of the following times of the day is the largest number of LEDs turned ON?

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
4. What is the maximum number of LEDs in my watch which can be turned ON at a given time of the day?

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?).
5. The leftmost hour and the leftmost minute LEDs are BOTH turned ON. How many times a day does this happen?

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).
6. As a single minute passes, what is the maximum number of LEDs which can switch from ON to OFF?

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.
7. Assuming that the only factor which determines the lifetime of a LED in my watch is the number of times it shifts between ON and OFF states and that all LEDs were installed at the same time, which is the LED that will last the longest time?

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.
8. What time is it when ONLY the 4 external LEDs in my watch are turned ON (i.e. leftmost and rightmost hour LEDs, leftmost and rightmost minute LEDs)?

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.
9. Which is the earliest time of the day when 7 LEDs in total are turned 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.
10. This last question may look short and sweet, but be warned not to lose yourself when performing the calculation - it's tricky. How many times a day exactly 3 LEDs in my watch are turned ON?