A Kakuro puzzle is like a crossword puzzle but with numbers instead of letters. The clue "n in k" tells you the k numbers in the row below the clue (or in the column to the right of the clue) add to n. Each cell can be filled in with any digit from 1 to 9, except that no digit is repeated within a clue. For example, to get "20-in-3", which means a sum of 20 in 3 digits, you would need the digits from one of these sets {3,8,9} {4,7,9} {5,6,9} {5,7,8} You can't use that 8+8+4= 20 because the 8 would be repeated. In the actual puzzle the cells would be filled in in some order, such as 479 or 947, etc., but ignoring these various permutations, we say there are 4 combinations that give "20-in-3". (a) List all combinations (sets of digits) that have the given clue-in-cell. 6-in-3 = 7-in-3 = 8-in-3= 10-in-4 = 11-in-4 = 12-in-4 = 30-in-4 = 29-in-4 = 28-in-4 = 15-in-5 = 16-in-5 = 22-in-6 = 24-in-3 23-in-3 22-in-3 = 45-in-9 = 42-in-8 = 42-in-7 = = (b) List all combinations (sets of digits) that have 20-in-4. Hint: there are 12 different possibilities. (c) Calculate the value of the intersection (n) cell in each case. Justify your answer. 3-in-2 4-in-2: 16-in-2 n 17-in-2: 15-in-5 n 29-in-4: 15-in-5 n 34-in-5: Possible extra credit: (d) Solve the Kakuro puzzles handed out in class, or harder ones you can find. (e) A kakuro is any clue-in-cell that has one unique combination. For example "15-in-5" is a kakuro because the only set of 5 distinct digits that adds to 15 is {1, 2, 3, 4, 5}. Pick and length n and list all kakuros of length n. Do for a variety of lengths. Hint: 2, 3, 8, and 9 are easiest.