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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?
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∙ 12y ago
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.
Wiki User
∙ 12y ago
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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
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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.
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how can you write 7 minutes after 3 on a digital clock
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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
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Four.
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A digital clock will have the greatest sum if added up at nine fifty nine. That would be three digits, not four.
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36 times. Hint: Seven, eight and nine can all be discarded.
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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?
hjalfvhbjhz
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