William Hindman
wdhindman at dejpolsystems.com
Mon Apr 26 11:30:25 CDT 2010
...sweet logic ...and wrong :)
...there goes my code boy hero :(
William
--------------------------------------------------
From: "Drew Wutka" <DWUTKA at marlow.com>
Sent: Monday, April 26, 2010 10:58 AM
To: "Access Developers discussion and problem solving"
<accessd at databaseadvisors.com>
Subject: Re: [AccessD] OT: Friday Puzzles
> Not possible that way....
>
> Look at it like this (visually):
>
> 100 soldiers.
>
> 70 lost an eye, so 30 did not lose an eye.
>
> 75 lost an ear, so 25 did not lose an ear.
>
> So let's look at this graphically, remember, we are looking at results
> for the same group of 100 soldiers, not different soldiers:
>
> 5| 10| 15| 20| 25| 30| 35| 40| 45| 50| 55| 60| 65| 70| 75| 80| 85| 90|
> 95|100|
> eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye| | | | |
> | |
>
> Above, I have shown a 'graph' of sorts, that shows groups of five. Now
> let's put in the ear group:
>
> 5| 10| 15| 20| 25| 30| 35| 40| 45| 50| 55| 60| 65| 70| 75| 80| 85| 90|
> 95|100|
> eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye| | | | |
> | |
> ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear| | | |
> | |
>
> Looking at it this way, we see that the MOST that have both is 70, and
> the most that have NOTHING is 25. But we don't care about who had
> nothing, having one or the other doesn't qualify for the generals medal
> of having all 4 (though we are only looking at two right now)
> 'conditions'. So with just the first two conditions, what is the least
> number that can have both? With our 'graph' here, we just have to slide
> one of them to the other side, like this:
>
> 5| 10| 15| 20| 25| 30| 35| 40| 45| 50| 55| 60| 65| 70| 75| 80| 85| 90|
> 95|100|
> | | | | |
> |eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|
> ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear| | | |
> | |
>
> Looking at it this way, we see that the minimum number that can have
> both conditions is 45. It doesn't matter how you span it, if you have
> 70% of a group with condition A, and 75% of the SAME group with
> condition B, you will have AT LEAST 45% of the group with BOTH Condition
> A and Condition B. (So that's 100%-(%withoutA+%withoutB), or
> 100%-(30%+25%)=45%)
>
> If we add the other two conditions, again, it doesn't matter which way
> they slide on the scale, they are bigger than the first two conditions,
> they will always overlap them:
>
> 5| 10| 15| 20| 25| 30| 35| 40| 45| 50| 55| 60| 65| 70| 75| 80| 85| 90|
> 95|100|
> | | | | |
> |eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|eye|
> ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear|ear| | | |
> | |
> | | |
> |arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|arm|
> leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg|leg| |
> | |
>
> Still at the magic number of 45%. Now in Arthur's original post, he did
> have a slight slip, by stating '85% of the soldiers had lost one leg',
> where the other three conditions all had clauses like 'at least one', or
> 'at a minimum', but if we were to take that literally, it's a
> mathematical impossibility to have 85% only losing one leg (and nothing
> else). To answer his riddle, he asks who, at a minimum, lost one eye,
> one ear, one arm, AND one leg, which is anywhere from 45% to 70%. The
> minimum to the maximum overlap of the conditions.
>
> This was a great puzzle for relational database developers. When it
> comes to Joins, we often thing of the overlapping circles, which
> represent different groups of data. But when it comes to data metrics,
> we sometimes have to look at our joins in different ways. In this case,
> 4 subsets all within one set. So Arthur's puzzle could easily have been
> a task a developer would have to figure out for a client, here it is in
> a real world example:
>
> Your client wants a database to track Returned Goods. There are 4
> possible conditions (A,B,C,D) in which a product will be returned. RG's
> can be returned for any combination of A,B,C, or D. One of the reports
> your client wants, is a report showing returned goods with all 4
> conditions, compared to the Max and Min that could have been returned
> with all four conditions based on the percentages returned with each
> condition. (ie, assuming Arthur's percentages, as RG reasons, and not
> injuries), a client might have 68% returned with all four conditions, so
> the report would show that his returned goods are hitting all 4
> conditions on the higher end of the possible range.
>
> Drew
>
>
> -----Original Message-----
> From: accessd-bounces at databaseadvisors.com
> [mailto:accessd-bounces at databaseadvisors.com] On Behalf Of Kevin
> Sent: Saturday, April 24, 2010 1:24 PM
> To: 'Access Developers discussion and problem solving'
> Subject: Re: [AccessD] OT: Friday Puzzles
>
> OK...
> I would like to revise and extend my remarks...
> Assuming an army of 100, 10 lost all 4
>
> 70 lost an eye
> So 30 did NOT lose an eye
> 75 lost an ear
> So 25 did NOT lose an ear
> 80 lost an arm
> So 20 did NOT lose an arm
> 85 lost a leg
> So 15 did NOT lose an leg
>
> The soldiers that retained at least one of the body parts is 90
> (30+25+20+15
> = 90) meaning that 10 lost all 4.
>
> Kevin Waddle
> "The time has come," the Walrus said,
> "To talk of many things:
> Of shoes--and ships--and sealing-wax--
> Of cabbages--and kings--
>
> -----Original Message-----
> From: accessd-bounces at databaseadvisors.com
> [mailto:accessd-bounces at databaseadvisors.com] On Behalf Of Shamil
> Salakhetdinov
> Sent: Saturday, April 24, 2010 10:22 AM
> To: 'Access Developers discussion and problem solving'
> Subject: Re: [AccessD] OT: Friday Puzzles
>
> That's wrong, and a bit(?)/plain(?) stupid, sorry. Any, takers? (I'm off
> till tomorrow's late evening/Monday).
>
> Thank you.
>
> --Shamil
>
> -----Original Message-----
> From: Shamil Salakhetdinov [mailto:shamil at smsconsulting.spb.ru]
> Sent: Saturday, April 24, 2010 7:30 PM
> To: 'Access Developers discussion and problem solving'
> Subject: RE: [AccessD] OT: Friday Puzzles
>
> 8925 medals.
>
> Correct?
>
> x = size of the army
> y = qty of soldiers who have lost one arm, one leg, one ear and one eye;
>
> y = 0.85*(1-0.8)*0.75*0.7x
>
> Assuming that army size is between 100,000+ and 150,000
> (
> http://www.secondworldwar.co.uk/units.html
> http://usmilitary.about.com/od/army/l/blchancommand.htm
> )
>
> the anwers would be
>
> foreach (int x in Enumerable.Range(100000,50001))
> {
> decimal y = 0.85m * (1.0m-0.8m) * 0.75m * 0.7m * x;
>
> if (y == (decimal)(int)y)
> Console.WriteLine("// SizeOfTheArmy={0:#,0}+, Medals={1} ",
> x, (decimal)(int)y);
> }
>
> // SizeOfTheArmy=100,000+, Medals=8925
> // SizeOfTheArmy=104,000+, Medals=9282
> // SizeOfTheArmy=108,000+, Medals=9639
> // SizeOfTheArmy=112,000+, Medals=9996
> // SizeOfTheArmy=116,000+, Medals=10353
> // SizeOfTheArmy=120,000+, Medals=10710
> // SizeOfTheArmy=124,000+, Medals=11067
> // SizeOfTheArmy=128,000+, Medals=11424
> // SizeOfTheArmy=132,000+, Medals=11781
> // SizeOfTheArmy=136,000+, Medals=12138
> // SizeOfTheArmy=140,000+, Medals=12495
> // SizeOfTheArmy=144,000+, Medals=12852
> // SizeOfTheArmy=148,000+, Medals=13209
>
> As we do not have the general's army size defined but we know that
> general
> wanted to reward teh fewest number of soldiers then we select the
> minimal
> appropriate army size = 100,000 soldiers, and then the answer will be
> 8925
> medals.
>
> Correct?
>
> Thank you.
>
> --Shamil
>
> <<< snip >>>
>
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