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Portraits of Pi etc

This week's problems are connected to the web site onethousandpaintings.com that is being reviewed. First read the review, explore the web site, and then try to solve these problems...

Question 1: Givin Salathe's pricing and value scheme, what is the most money and least money that he could make, assuming all of the paintings are sold?

Question 2: For which numbers is it possible to buy the painting N for $N, where the cost could be associated with any of the discounted percentages?

Question 3: Which set of numbers--the primes or the composites--collectively have the greatest value? Remember that the number 1 is in neither set.

Question 4: Tosh Cooey, a big fan of the number pi (i.e. 3.14159265...), has purchased the three paintings..


But, in a note to Salathe, Cooey wants to extend this sequence for pi and wonders "what the longest possible sequence is using only your paintings." Remember that you only have the numbers 1 - 1000 to work with. Why is the limit 603 digits? Stefan Urech provided a solution using 220 paintings to create those first 603 digits of Pi, while Charlie from Colorado was able to do it using 215 paintings. Can you do better?

 


Hint: Sorry, no hints available....as I am still playing with the problems myself.

 


Solution Commentary: Sorry, no solution commentary available....as I am still playing with the problems myself. That's the difficulty when you pose your own problems...you also have to (i.e. get to) solve them!