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How many times in a twelve hour period does the sum of the digits on a digital clock equal six and prove it?
notation: natural numbers = 0,1, 2, 3, 4, 5, ....., (some define it without the zero, though) <= means smaller than or equal to, {} is set notation and means a set of numbers : (such that) then some condition. For example {x: x is not a duck} is the set of all things not a duck.
Our goal is to prove that there are 21 different times. let x1 = hours, x2 = tens of minutes, x3 = minutes. We are going to prove the statement about the set {x1, x2,x3: 1<=x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. It will be taken by assumption that this set is the set of digital clock combinations that add up to 6. So then, we must prove that there are unique 21 elements in the set {x1 + x2 + x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. {x1 , x2 , x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6} = {x1 , x2 , x3 : 1<= x1 <= 6, 0<= x2<=5, 0<=x3 <= 5, x1 + x2 + x3 = 6} because x3<=6, and because if x1 >=1, then x2 + x3 <=5, and x3, x2 >= 0 , so surely x3, x2 <= x5. Either x1 = 1, 2, 3, 4, 5, or 6. Next, x1 + x2 + x3 = 6, so x2 + x3 = 6 - x1. There are n+1 natural numbers between 0 and n (I'm being lazy and not proving this, but the proof would be so much longer if I proved it), and since 0 <= x2 <= 5 <= 6-x1, there are at most 6-x1+1 values of x2 for each value of x1. When x1 = 1, there are a maximum of 6, when x1 = 2, there are 6-2+1 = 5, when x1 = 3, there are 6-3+1 = 4, when x1 = 3, there are 3, then 2, and then 1. Summing this up gives us a maximum of 21. So it is at most 21 and at least 21, so exactly 21.
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How many times in a 12 hour period does the sum of the digits on a digital clock equal 6?
36 times
A digital clock sHow is either 3 or 4 digits at a time at what time do the digits have the greatest sum?
A digital clock will have the greatest sum if added up at nine fifty nine. That would be three digits, not four.
How many times in a 12 hour period does the sum of the digits on a digital clock equal 6 describe what you did?
36 times. Hint: Seven, eight and nine can all be discarded.
How many times will the digit 7 appears in a digital clock in 24 hours?
Oh, what a happy little question! In a 24-hour day, the digit 7 will appear 8 times on a digital clock. You can find it in times like 07:07, 17:37, and 23:57. Just imagine those sevens dancing across the clock, bringing joy to each hour.
How many times in each 24 hour period do each all 6 digits change simultaneously?
In a 24-hour period, all 6 digits on a digital clock change simultaneously 22 times. This occurs every hour, except for the first hour of the day when the leading zero is not displayed. The digits change simultaneously when transitioning from 9:59 to 10:00, 10:59 to 11:00, and so on until 8:59 to 9:00. This pattern repeats 22 times in a 24-hour period.
How many times in a twelve hour period does the sum of the digits on a digital clock equal six?
36 times
How many times in a 12 hour period does the sum of the digits on a digital clock equal 6?
36 times
How many times does a digital clock show the same digits at a time in a twenty four hour period?
Four.
In any twelve hour period how many times will the digits of a digital clock be in strictly increasing order?
The answer is 65. Start with 1:23, 1:24, 1:25, etc. Do this for each hour. Don't for get the 12th hour....12:34......etc
A digital clock sHow is either 3 or 4 digits at a time at what time do the digits have the greatest sum?
A digital clock will have the greatest sum if added up at nine fifty nine. That would be three digits, not four.
How do you calculate minimum clock period in a digital circuit?
If you have the Maximum clock frequency, then you can figure out the minimum clock period using this formula: 1/(minimum clock period) = (Maximum clock frequency).
How many times does the sum of the digits on a digital clock equal 8 on a 24-hour military clock?
There are 93 such events.
At what time is the sum of the digits on a digital clock the greatest?
The sum of the digits on a digital clock is the greatest when the time is 9:59. At this time, the sum of the digits is 9 + 5 + 9 = 23. This is the highest possible sum because the maximum value for each digit on a digital clock is 9.
How many times in a 12 hour period does the sum of the digits on a digital clock equal 6 describe what you did?
36 times. Hint: Seven, eight and nine can all be discarded.
What is twenty five to two as it would appear on a twelve hour digital clock?
1:35
On a digital clock how many palindromes show up in a 24 hour period?
There are exactly 114 palindromes on a digital clock in a 24 hour period. I was asked to do this problem for homework and so theres your answer.
How many times in a 12 hour period does the sum of the digits on a digital clock equal 6 try to think of a way to solve this without going through every single time?
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