Back to more routine stuff. The Price Is Right played ``Pay The Rent'' last Tuesday, so let me put that on record. (The Price Showcase Showdown stuff I figure to have tomorrow barring more urgent news.) For this lineup the prizes were a box of raisins ($3.99); one of those silly energy drinks ($6.99); some cocktail sauce ($2.49); a toothbrush ($2.19); oven cleaner ($4.99); and soap ($2.99).
The contestant picked the toothbrush for the lowest level (level total $2.19), which is fine for a just-put-the-prizes-in-ascending-cost-or
I'm done working this stuff out by hand; while _fluffy wrote a one-line Prolog code for it, I wrote a more verbose Matlab/Octave version and can say there are two winning paths for this. The first: start with the oven cleaner ($4.99); on the next level the cocktail sauce and soap (level $5.48), on the next the toothbrush and the raisins (level $6.18), and finally the energy drink ($6.99). The other path is to again start with the oven cleaner ($4.99); on the next level the toothbrush and soap (level $5.18); on the next the cocktail sauce and raisins (level $6.48); and finally the energy drink ($6.99).
Finding that there are multiple solutions for this one too --- and I'm not surprised considering the problem --- makes it a little harder to say definitively what the level ranges are. But the price ranges so far have been $3.90 and $4.80 (getting more generous). Taking the more generous range in levels from the last time and this we have ranges of $3.20 and $2.00.
Trivia: Pasteur's experiments for disproving spontaneous generation were decribed in his notes of 7 May, 3 September, and 5 November 1861, and published in July 1863 as Mémoire sur les corpuscules organisés qui existent dans l'atmosphere. Source: Louis Pasteur, Patrice Debré, Translated by Elborg Forster.
Currently Reading: As She Climbed Across The Table, Jonathan Lethem.