The Binary Watch

15 Points Per Correct Answer - No time limit  

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? Answer: (an odd two-digit number, please answer in decimal)

2. In which of the following times of the day NO two adjacent LEDs are turned ON (i.e. adjacent in a given row)? 11:42 11:43 10:43 10:42

3. In which of the following times of the day is the largest number of LEDs turned ON? 15:47 12:09 07:27 19:43

4. What is the maximum number of LEDs in my watch which can be turned ON at a given time of the day? Answer: (one digit, please answer in decimal)

5. The leftmost hour and the leftmost minute LEDs are BOTH turned ON. How many times a day does this happen? Answer: (a three-digit number, please answer in decimal)

6. As a single minute passes, what is the maximum number of LEDs which can switch from ON to OFF? Answer: (one digit, please answer in decimal)

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 leftmost minute LED The rightmost hour LED The rightmost minute LED The leftmost hour LED

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)

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)

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? Answer: (an even three-digit number, please answer in decimal)