Counting occurrences of an intermittent event depending on start, end and frequency
$begingroup$
I am sorry if this is a trivial question (I am really bad at math ;-)), but I cannot manage to find a convincing mathematical solution for it.
So, let's suppose events that occur intermittently along the days:
Event A occurs every 2 days, starts on day 1
Event B occurs every 2 days, starts on day 2
Event C occurs every 3 days, starts on day 3
etc.
Visually presented:
days 1 2 3 4 5 6 7 8 ...
A * * * *
B * * * *
C * *
Now, I want to compute how many events of each observer will see, depending on the day they arrive and the day they leave.
Thus, I have the following variables:
event
frequency: 1/2, 1/3...
startingDay: 1, 2, 3...
observer
firstDay: 1, 2, 3...
lastDay: 6, 7, 8...
totalDays = lastDay - firstDay + 1
Is there a formula that could easily compute for each observer how many events of each type he will see? I tried combining rounding (flooring totalDays*frequency) + some modulo, but I cannot seem to find the hang of it.
algebra-precalculus
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
$endgroup$
add a comment |
$begingroup$
I am sorry if this is a trivial question (I am really bad at math ;-)), but I cannot manage to find a convincing mathematical solution for it.
So, let's suppose events that occur intermittently along the days:
Event A occurs every 2 days, starts on day 1
Event B occurs every 2 days, starts on day 2
Event C occurs every 3 days, starts on day 3
etc.
Visually presented:
days 1 2 3 4 5 6 7 8 ...
A * * * *
B * * * *
C * *
Now, I want to compute how many events of each observer will see, depending on the day they arrive and the day they leave.
Thus, I have the following variables:
event
frequency: 1/2, 1/3...
startingDay: 1, 2, 3...
observer
firstDay: 1, 2, 3...
lastDay: 6, 7, 8...
totalDays = lastDay - firstDay + 1
Is there a formula that could easily compute for each observer how many events of each type he will see? I tried combining rounding (flooring totalDays*frequency) + some modulo, but I cannot seem to find the hang of it.
algebra-precalculus
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
$endgroup$
add a comment |
$begingroup$
I am sorry if this is a trivial question (I am really bad at math ;-)), but I cannot manage to find a convincing mathematical solution for it.
So, let's suppose events that occur intermittently along the days:
Event A occurs every 2 days, starts on day 1
Event B occurs every 2 days, starts on day 2
Event C occurs every 3 days, starts on day 3
etc.
Visually presented:
days 1 2 3 4 5 6 7 8 ...
A * * * *
B * * * *
C * *
Now, I want to compute how many events of each observer will see, depending on the day they arrive and the day they leave.
Thus, I have the following variables:
event
frequency: 1/2, 1/3...
startingDay: 1, 2, 3...
observer
firstDay: 1, 2, 3...
lastDay: 6, 7, 8...
totalDays = lastDay - firstDay + 1
Is there a formula that could easily compute for each observer how many events of each type he will see? I tried combining rounding (flooring totalDays*frequency) + some modulo, but I cannot seem to find the hang of it.
algebra-precalculus
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
$endgroup$
I am sorry if this is a trivial question (I am really bad at math ;-)), but I cannot manage to find a convincing mathematical solution for it.
So, let's suppose events that occur intermittently along the days:
Event A occurs every 2 days, starts on day 1
Event B occurs every 2 days, starts on day 2
Event C occurs every 3 days, starts on day 3
etc.
Visually presented:
days 1 2 3 4 5 6 7 8 ...
A * * * *
B * * * *
C * *
Now, I want to compute how many events of each observer will see, depending on the day they arrive and the day they leave.
Thus, I have the following variables:
event
frequency: 1/2, 1/3...
startingDay: 1, 2, 3...
observer
firstDay: 1, 2, 3...
lastDay: 6, 7, 8...
totalDays = lastDay - firstDay + 1
Is there a formula that could easily compute for each observer how many events of each type he will see? I tried combining rounding (flooring totalDays*frequency) + some modulo, but I cannot seem to find the hang of it.
algebra-precalculus
algebra-precalculus
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
edited Dec 7 '18 at 15:44
Serge B.
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
asked Dec 7 '18 at 15:32
Serge B.Serge B.
1013
1013
add a comment |
add a comment |
1 Answer
1
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$begingroup$
After decomposing the problem and trying every possible combination for a few days, I think I found the solution. At least, it seems to work for every possible case I can think of. It might be possible to reduce it, but at least, it works.
numberOfEventsSeen = ceil( (totalDaysOfObservation - ( (eventFrequency - (
(dayOfArrival - 1 - eventStartingDay - 1) % eventFrequency) )
% eventFrequency) ) / eventFrequency )
where
ceil() = ROUNDUP in Excel for instance
totalDaysOfObservation = dayOfDeparture - dayOfArrival - 1
eventFrequency = 2 (if event happens every 2 days), 3, etc.
(Note: sorry if this is by no means a normal mathematical notation ;-))
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
After decomposing the problem and trying every possible combination for a few days, I think I found the solution. At least, it seems to work for every possible case I can think of. It might be possible to reduce it, but at least, it works.
numberOfEventsSeen = ceil( (totalDaysOfObservation - ( (eventFrequency - (
(dayOfArrival - 1 - eventStartingDay - 1) % eventFrequency) )
% eventFrequency) ) / eventFrequency )
where
ceil() = ROUNDUP in Excel for instance
totalDaysOfObservation = dayOfDeparture - dayOfArrival - 1
eventFrequency = 2 (if event happens every 2 days), 3, etc.
(Note: sorry if this is by no means a normal mathematical notation ;-))
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
$endgroup$
add a comment |
$begingroup$
After decomposing the problem and trying every possible combination for a few days, I think I found the solution. At least, it seems to work for every possible case I can think of. It might be possible to reduce it, but at least, it works.
numberOfEventsSeen = ceil( (totalDaysOfObservation - ( (eventFrequency - (
(dayOfArrival - 1 - eventStartingDay - 1) % eventFrequency) )
% eventFrequency) ) / eventFrequency )
where
ceil() = ROUNDUP in Excel for instance
totalDaysOfObservation = dayOfDeparture - dayOfArrival - 1
eventFrequency = 2 (if event happens every 2 days), 3, etc.
(Note: sorry if this is by no means a normal mathematical notation ;-))
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
$endgroup$
add a comment |
$begingroup$
After decomposing the problem and trying every possible combination for a few days, I think I found the solution. At least, it seems to work for every possible case I can think of. It might be possible to reduce it, but at least, it works.
numberOfEventsSeen = ceil( (totalDaysOfObservation - ( (eventFrequency - (
(dayOfArrival - 1 - eventStartingDay - 1) % eventFrequency) )
% eventFrequency) ) / eventFrequency )
where
ceil() = ROUNDUP in Excel for instance
totalDaysOfObservation = dayOfDeparture - dayOfArrival - 1
eventFrequency = 2 (if event happens every 2 days), 3, etc.
(Note: sorry if this is by no means a normal mathematical notation ;-))
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
$endgroup$
After decomposing the problem and trying every possible combination for a few days, I think I found the solution. At least, it seems to work for every possible case I can think of. It might be possible to reduce it, but at least, it works.
numberOfEventsSeen = ceil( (totalDaysOfObservation - ( (eventFrequency - (
(dayOfArrival - 1 - eventStartingDay - 1) % eventFrequency) )
% eventFrequency) ) / eventFrequency )
where
ceil() = ROUNDUP in Excel for instance
totalDaysOfObservation = dayOfDeparture - dayOfArrival - 1
eventFrequency = 2 (if event happens every 2 days), 3, etc.
(Note: sorry if this is by no means a normal mathematical notation ;-))
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
answered Dec 12 '18 at 10:07
Serge B.Serge B.
1013
1013
add a comment |
add a comment |
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