HW1 due Wednesday, May 12 6.1: 1,3,7,11,15,17,21,35,41,51,53, 6.2: 3,5,7,11,17,25,33,42 HW2 due Wednesday, May 19 6.3: 4,7,11,18,21,37,38,42 6.4: 2,7,13,16,29,37 6.5: 1,2,3,7,11,14 HW3 due Wednesday, May 26 6.5: 15,20,22,51,61 6.6: 5,7,8 7.1: 5,7,8,14,17,18,21,33,36,42 HW4 due Wednesday, June 2 (extension: Friday, June 4) A) 7.2: 1,2,3,5,7,9,18,24,27,31 B) Find a 7-letter word with 4 of the same letter and 3 other distinct letters which does NOT require a blank to be formed with scrabble tiles. (use 7all.txt) Form the alphabetized string from this word, and then also find all the alphabetized strings including 1 or 2 blanks associated to this string. Finally, find the probability that a random draw of 7 tiles from the bag of 100 results in the ability to spell this word. C) Find a 7-letter word with 4 of the same letter and 3 other distinct letters which DOES require a blank to be formed with scrabble tiles. (use 7all.txt) Form the alphabetized string from this word, and then also find all the alphabetized strings including 1 or 2 blanks associated to this string. Finally, find the probability that a random draw of 7 tiles from the bag of 100 results in the ability to spell this word. HW 5 due Wednesday, June 16 A) 7.4: 2,3,5,8,10,17,19 B) Find a 7-letter word with 3 of the same letter, 2 of a second letter, and 2 of a third letter, which does NOT require a blank to be formed with scrabble tiles. (use 7all.txt) Form the alphabetized string from this word, and then also find all the alphabetized strings including 1 or 2 blanks associated to this string. Finally, find the probability that a random draw of 7 tiles from the bag of 100 results in the ability to spell this word. C) Find a 7-letter word with 3 of the same letter, 2 of a second letter, and 2 of a third letter, which DOES require a blank to be formed with scrabble tiles. (use 7all.txt) Form the alphabetized string from this word, and then also find all the alphabetized strings including 1 or 2 blanks associated to this string. Finally, find the probability that a random draw of 7 tiles from the bag of 100 results in the ability to spell this word. D) For the domineering game played on a 2x5 rectangle (2 rows, 5 columns) determine the following: i) Draw the game tree and label the probability for each branch. ii) Who has a winning strategy playing first (Left or Right)? Same question for playing second. iii) For random play determine P(Lwpf), P(Rwps), P(Rwpf), and P(Lwps). HW 6 due Wednesday, June 23 A) 7.4: 27,28,30,44; 8.4: 2,10,13,14 HW 7 due Wednesday, July 7 1.1: 15,16,24,30,37 1.2: 11,12,33,44 1.4: 7,8,13,14,16,20,30,37 1.5: 2,11,24 HW 8 due Wednesday, July 14 A) 1.7: 27, 36, 40 B) Attempt to prove by induction on game tree height that all combinatorial games are impartial. State and prove the base case. State the induction hypothesis. Show why the induction step fails.