problem solving - university of dayton
TRANSCRIPT
1
Problem Solving
• Goals• Objects / givens• Operations / transformations• Constraints / obstacles
Types of Problems
• Well-defined• Ill-defined
2
Problem Solving Process
1. Form initialproblem
representation
2. Try to planpotentialsolution
4. Execute planand check
results
3. Try toreformulate
problem
Done!
Stuck!(return to step3 after a break)
then success
if plan fails
if fa
il
if success
if fail
Initial Representation
One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. A narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended at varying rates of speed, stopping many times along the way to rest and eat dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation he began his journey back along the same path, starting at sunrise and again walking at variable speeds, with many pauses along the way. His average speed descending was, of course, greater than his average climbing speed. Show that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day.
2 3 4 51 6 87 9
Initial RepresentationEach of the digits 1 through 9 is written on a separate piece of paper. Two players draw digits alternately. As soon as either player gets any three digits that sum to 15, that player wins. If all nine digits are drawn without a win, then the game is a draw.
Player 1:0
Player 2:0
294
753
618
3
Types of Representations
PSY 502
PSY 217
PSY 529,531Thurs.
PSY 216
PSY 101
PSY 522Wed.
PSY 502
PSY 217
PSY 529,531Tues.
PSY 216
PSY 101
Fri.
PSY 216
PSY 101
PSY 522Mon.
SJ 003SJ 231SJ 325
Plan a Solution
• Algorithm vs. heuristic
• Some heuristics:– Generate-test method– Simple search (e.g. hill climbing)– Means-ends analysis– Working backward
Plan a Solution:Remove Unnecessary Constraints
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Plan a Solution:Applying an Analogy
Blocks that Hinder Problem Solving
25376288183391572034923631459205216429451043183
99251631421003127211
CBAAmount to get
Capacity of Jars
Blocks that Hinder Problem Solving
5
Blocks that Hinder Problem Solving
Analyzing Problem-Solving Behavior: Verbal Protocols
• Solve:CROSS+ROADS------DANGER
1. Experimenter: R is 6:C60SS+6OADS------DANGE6
2. Since R is 6 and the two S’s are equal…
3. S must be equal to 3, or 8.4. And D must be equal to 1…5. Because C plus R can’t be
greater than 19…6. Or greater than 16 in this
case.7. So D must be a 1.
8. Would you make D a 1?9. Experimenter: D is 1.10. And seeing that two S’s are
equal…11. They must be either 3 or 8…12. If they are 8…13. Then E would be 0.14. If they are 3…15. Then E would be 4.16. So let’s try the S’s as 8.17. Could you make the S an 8?18. Experimenter: S is 8.19. That would make E a 0.20. Would you make E a 0?21. Experimenter: E is 0.
Analyzing Problem-Solving Behavior: Verbal Protocols
1 R = 6
2 2 S’s are =
3 S = 3 or 8
4 D = 1
10 11 S = 3 or 8
12 If S=8, E=0
14 If S=3, E=4
15 16 Set S = 8
19 Set E = 0