Did Pólya say, "can" or "cannot"?
Solution 1:
I will quote exactly what as I see on my version of the book (Second Edition, 1957) on page 114.
If you cannot solve the proposed problem do not let this failure afflict you too much but try to find consolation with some easier success, try to solve first some related problem; then you may find courage to attack your original problem again. Do not forget that human superiority consists in going around an obstacle that cannot be overcome directly, in devising some suitable auxiliary problem when the original one appears insoluble.
From all the sources I've read, it doesn't seem like he explicitly wrote the commonly known quote on his book.
Solution 2:
Possible (indirect) reference, from source:
- Gerald L. Alexanderson, The random walks of George Pólya (2000), page 116:
The phrases that Pólya uses (and lists in his "short dictionary of heuristic" in How to solve it) have eneterd the language of mathematics and mathematics education: "Could you restate the problem ?": [...] Another suggestion is: if one cannot solve the proposed problem can one find a problem (preferably related to the original!) that one can solve [emphasis mine] ?
In the "How to solve it" list, page xvii, we have :
If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem ?
So, it seems that Polya's original direction was : "search for an easier problem"...
Solution 3:
I once encountered George Polya, going up the elevator in the Stanford Library! I told him what a great movie actor he was. (We had seen several of his instructional videos in my combinatorics class.) At least I got a smile out of him. I hope I am not giving away my age with this!
My edition of HTSI does not have Conway's forward; it is really old, the paper has that funny smell, and inside it says "second edition" and "second printing 1973" from Princeton University Press.
Now for the question: I was unable to find any statement from Polya to "search for an easier problem". However, I did find a section on "If you cannot solve the proposed problem", p. 114. There Polya advises to "try to solve first some related problem". He suggests inventing such a problem.
Besides this, he suggests working a related problem (p. 98), Generalization (p. 108), A problem related to yours and solved before (p. 119), Variation of the Problem (p. 209).
However, he also suggests the opposite, Inventor's Paradox (p. 121), wherein a grander problem that includes the original task is attacked. Here the goal is to expand one's vision and think in new directions.
I hope this helps; Polya may be considered the Sun Tzu of mathematics for this work.