| Problem Set |
Section |
Problems |
|---|---|---|
| 02 | * | Tom is playing Mastermind with a friend and, unlike when the game was demonstrated in class, you do not know the hidden “code.” The eligible colors are Blue, Green, Red, Yellow, Orange and Pink (BGRYO and P). Here are Tom's first two attempts to break the code, along with the responses of the code-setter (A ‘Black’ means a color appears and is in the right position; a ‘White’ means a color appears in the wrong position). 1st move: B G R Y Response: 1 Black, 1 White 2nd move: O P B Y Response: 1 Black At this moment, Tom claims he knows that there are no more than three colors which appear in the secret code. Is he correct? Explain why or why not. Note: If you feel you could use some more experience as to how the game is played, try it out at the website http://www.mathgym.com.au/htdocs/logarc.htm Here is Tom's next move: 3rd move: B B B B Response: 3 Blacks Given the response he got, this seems to have been a good move. Did Tom have a reasonable expectation that the secret code might, indeed, contain all blue pegs? If so, explain why. If not, then what might he have hoped to learn from this move? Given the three moves already made, indicate all of the possibilities that remain for the secret code. (Hint: A correct list contains exactly three possible codes.) |
| p. 26 | 3 -- The profit | |
| 5 -- It's in the box. You are permitted to read the hint in Section 1.2 for Story 8 (“Dot of Fortune”) and the solution in Section 1.3 as well, as this is a similar kind of problem. (Please do not read the hints or solutions for the other stories, however.) | ||
| 6 -- Lights out | ||
| 8 -- Cannibals and missionaries | ||
| 9 -- Whom do you trust | ||
| You need not do all three of 6, 8 and 9. Select two of them. (If you have heard one of them before, select the other two.) If you are having difficulty, hints are provided on pp. 31-32. Please hold off looking at a hint until you have mulled over the problem for a full day (and overnight), consciously implementing the “Lessons for Life” found on p. 25. | ||
| n | manditory problem |
| (n) | helper problem |
| [n] | ungraded problem |
| {n} | optional problem |