Sunday, September 1, 2019

Digital Clock Problem

The clock below uses columns of dots to represent the time, in minutes and hours.  What time does the clock read?



Use the clues below to decode the number system and read the time on the clock above.

Clues:




Here is the solution:

Each column represents a different power of 4.  And the number of dots tells you how many 1s, 4s, and 16s you have.  One way to see this is to start with the 8:04 clock and focus on the minutes.  It takes only one dot to make the number :04, so the single dot must have that value.  Then look at the 9:20 clock and again focus on the minutes.  It takes 2 dots to make :20.  One of those dots, we now know, is worth 4, so the other must be worth 16.  

All together the dots on the mystery clock represent:


4 + 4 + 1 + 1 hours, and
16 + 1 + 1 + 1 minutes, so

10:19