Problem-solving 3

another important part of problem-solving is

how to represent the problem in an effective way

in many cases, the real problem is

to figure out what even is the problem that we’re trying to solve

ex: available moves? result of these moves?

The triangle in circle problem in class illustrates that going from “no rectangle” to

'“with rectangle” to help solve the problem is a change in the way that people represent the problem (to help them solve the problem in a more effective way)

sometimes, solving a problem is a matter of

suddenly finding the right perspective

Mutilated checkerboard problem

removing 2 opposite corners of the board, leaving 62 squares and 31 domino pieces. Q: can we cover these 62 squares exactly using 31 domino pieces?

answer to Mutilated checkerboard problem:

hard no, bc remove 2 squares of the same color (red). Whichever way you put a domino piece on this board, it always covers 1 black and 1 red

Russian marriage problem

64 bachelors (32 men, 32 women) → 2 men died leaving 62 bachelors. Q: can the matchmaker still arrange 31 (heterosexual marriage for these 62 bachelors?)

Answer to the Russian marriage problem

easy no, bc 32 women and 30 men can’t match for heterosexual marriage

now we can see that these 2 problems are the same and have the same answer, Newell and Simon would say

these problems have the same problem space and solution

Mutilated checkerboard problem is harder than the Russian marriage problem bc

we are inclined to represent the 2 problems in different ways (looking at them from different perspectives)

2 squares of the same color removed was available to you, but

you may not have notice it

the face that 2 men die was

harder to miss

the fact that a domino always covers 2 squares of the opposite color was available to you, but you

may have not notice it

but the fact that a heterosexual marriage involves a man and a woman is

obvious