“91974˙CH01˙ﬁnal” — 2012/12/14 — 13:55 — page6—#6
6 CHAPTER 1 Introduction
You will understand and apply abstraction.
You will learn to think and communicate more clearly.
1.4 Problem-Solving Strategies
Problem solving happens on three diﬀerent levels:
Strategy: A high-level idea for ﬁnding a solution.
Tactics: Methods or patterns that work in many diﬀerent settings.
Tools: Speciﬁc tricks and techniques that are used in speciﬁc situations.
Paul Zeitz [Zei99] provides us with a helpful analogy for illustrating the three diﬀerent
levels of problem solving:
You are standing at the base of a mountain, hoping to climb to the summit.
Your ﬁrst strategy may be to take several small trips to various easier peaks
nearby, so as to observe the target mountain from diﬀerent angles. After this,
you may consider a somewhat more focused strategy, perhaps to try climbing
the mountain via a particular ridge. Now the tactical considerations begin:
how to actually achieve the chosen strategy. For example, suppose that our
strategy suggests climbing the south ridge of the peak, but there are snowﬁelds
and rivers in our path. Diﬀerent tactics are needed to negotiate each of these
obstacles. For the snowﬁeld, our tactic may be to travel early in the morning
while the snow is hard. For the river, our tactic may be scouting the banks for
the safest crossing. Finally, move into the most tightly focused level, that of
tools: speciﬁc techniques to accomplish specialized tasks. For example, to cross
the snowﬁeld we may set up a particular system of ropes for safety and walk
with ice axes. The river crossing may require the party to strip from the waist
down and hold hands for balance. These are all tools. They are very speciﬁc.
You would never summarize, “To climb the mountain we had to take our pants
oﬀ and hold hands,” because it was a minor—though essential—component of
the entire climb. On the other hand, strategic and sometimes tactical ideas are
often described in your summary: “We decided to reach the summit via the
south ridge and had to cross a diﬃcult snowﬁeld and a dangerous river to get
to the ridge.”