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A Maths Problem ...
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... today is something of a 'mirabile die' as my old Latin teacher would have said.
I have two sources of income - one pays every four weeks on a Tuesday, the other pays on the 15th of every month - and today the two days coincided - I am (temporarily) 'in funds' :)
But (as I love playing with numbers) I then started thinking about how often this must happen - a simple spreadsheet produced the previous and next dates (just keep either adding or subtracting 28 days to today's date for a list) ...
But there didn't seem to be an obvious pattern - so I had a very large cup of coffee and attempted a bit more analysis.
I now have the period over which the sequence repeats and an answer for how often the 15th and 'every fourth week' coincide.
Q1 : What is the period for repeats
Q2 : How often do the days coincide in that period
Q3 : Does it matter that it's the 15th?
If that''s too easy (hello jim360) then try
Q4 : What if I was paid on the last calendar day of each month - how often would that coincide with the 'every fourth week' sequence.
Happy Puzzling
SD xx
I have two sources of income - one pays every four weeks on a Tuesday, the other pays on the 15th of every month - and today the two days coincided - I am (temporarily) 'in funds' :)
But (as I love playing with numbers) I then started thinking about how often this must happen - a simple spreadsheet produced the previous and next dates (just keep either adding or subtracting 28 days to today's date for a list) ...
But there didn't seem to be an obvious pattern - so I had a very large cup of coffee and attempted a bit more analysis.
I now have the period over which the sequence repeats and an answer for how often the 15th and 'every fourth week' coincide.
Q1 : What is the period for repeats
Q2 : How often do the days coincide in that period
Q3 : Does it matter that it's the 15th?
If that''s too easy (hello jim360) then try
Q4 : What if I was paid on the last calendar day of each month - how often would that coincide with the 'every fourth week' sequence.
Happy Puzzling
SD xx
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"You need to get out more"....Barmaid? No he doesn't!!!
I was going out yesterday and asked Dave if he wanted to come with me.....he needed petrol in his car so he said he would drive......
When he picked me up he spent ten minutes in my hall "discussing" this.........then started mulling it over......aloud....in the car......
No.......he needs to stay at home when he's playing with his numbers....... ;-)
I was going out yesterday and asked Dave if he wanted to come with me.....he needed petrol in his car so he said he would drive......
When he picked me up he spent ten minutes in my hall "discussing" this.........then started mulling it over......aloud....in the car......
No.......he needs to stay at home when he's playing with his numbers....... ;-)
Apart from leap years there is anothe rpossible complication - and that is what happens if the 15th falls at a weekend- are you paid early, on time or late?
What would be a simple problem if every month were teh same length becomes more complicated by the unequal distribution of month lengths, and with leap years to factor in, the numbers of coincident dates will vary from year to year.
Without any calculations at this stage I would say it happens no more than around once every 24 months
What would be a simple problem if every month were teh same length becomes more complicated by the unequal distribution of month lengths, and with leap years to factor in, the numbers of coincident dates will vary from year to year.
Without any calculations at this stage I would say it happens no more than around once every 24 months
"...doesn't help that some idiot decided that months shouldn't have the same number of days ... "
I expect the idiot was faced with the problem that there are 365 days in a year (fixed because of the time it takes the Earth to orbit the Sun). You cannot divide 365 equally by twelve. Of course we don't have to have twelve months. The trouble is you cannot divide 365 equally by any number except five or seventy-three, so we can have either five months of 73 days or seventy-three months of 5 days. A bit of a no-no really.
The answer would be to decimalise the calendar and time. I prepared a paper on this once. It used 100 days in a year with ten months of ten days each. Each day would be of 10 hours (each hour being subdivided into a 100 minutes made up of 100 seconds). I worked out that Christmas Day fell on June 5th and that the New Year would be rung in at 4:29pm on September 13th (September 19th in Leap Years). With only ten months to play with I decided to do away with January and February as they are the coldest.
I expect the idiot was faced with the problem that there are 365 days in a year (fixed because of the time it takes the Earth to orbit the Sun). You cannot divide 365 equally by twelve. Of course we don't have to have twelve months. The trouble is you cannot divide 365 equally by any number except five or seventy-three, so we can have either five months of 73 days or seventy-three months of 5 days. A bit of a no-no really.
The answer would be to decimalise the calendar and time. I prepared a paper on this once. It used 100 days in a year with ten months of ten days each. Each day would be of 10 hours (each hour being subdivided into a 100 minutes made up of 100 seconds). I worked out that Christmas Day fell on June 5th and that the New Year would be rung in at 4:29pm on September 13th (September 19th in Leap Years). With only ten months to play with I decided to do away with January and February as they are the coldest.
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