Wk
Strand
Assignment
What the week is
01
Steps & Cost
What Is a Step?
Before you can say one method is better, you have to say what you are counting.
02
Steps & Cost
Two Sorts, Counted
Two methods, the same cards, the same finish, and very different bills.
03
Steps & Cost
Sorting by Splitting
Cut the pile in half, sort both halves, then zip them together.
04
Steps & Cost
Searching a Sorted List
Halving is so much better than looking that the numbers stop feeling real.
05
Number Structure
Doubling and Halving
The numbers behind last week. They get very big very fast.
06
Steps & Cost
The Greedy Rule
Take the biggest that fits, then do it again. Simple, fast, and usually right.
07
Steps & Cost
When Greedy Fails
Change three coins and the simple rule starts giving wrong answers.
08
Dots & Lines
Shortest Path With Costs
Not the fewest roads. The cheapest total, in dollars and cents.
09
Dots & Lines
The Cheapest Network
Two completely different methods. Same answer, every time.
10
Steps & Cost
Packing the Boxes
Same parcels, same boxes. Change the order they arrive in and you need a whole extra box.
11
Steps & Cost
Scheduling the Jobs
Six jobs, thirteen days of work, and it can all be done in ten.
12
Steps & Cost
Method Fair
One problem, four methods, one bill each.
13
Logic & Proof
Case Files
Everything from the first twelve weeks, priced.
14
Ways of Counting
Counting on a Grid
Streets on a coordinate grid, and only two directions allowed.
15
Ways of Counting
Paths That Avoid a Block
Count everything, then subtract the ones you did not want.
16
Ways of Counting
Two Circles, Then Three
Add the three clubs and you have counted some children twice and some three times.
17
Ways of Counting
Counting the Leftovers
Sometimes the fastest way to count what you want is to count what you do not.
18
Fractions
Sharing Fairly
Dividing by a fraction is a counting question in disguise.
19
Fractions
A Fraction of a Fraction
Cut a square one way, then the other. The overlap is the answer.
20
Number Structure
Powers and Place Value
Every column is ten times the one on its right, and that is a rule you can push around.
21
Number Structure
Base Five
A whole number system with only five digits. Not a code, a way of counting.
22
Number Structure
Carrying in Base Five
Column addition works in any base. Only the moment you carry changes.
23
Steps & Cost
How a Machine Adds
Two digits, one carry, and that is the entire arithmetic of a computer.
24
Steps & Cost
Logic Gates
Three tiny machines. Wire them together and you get last week’s adding.
25
Logic & Proof
Puzzle Fair
A little of everything from Weeks 14 to 24.
26
Dots & Lines
Flow Through a Network
Water, not routes. How much can you push from one end to the other?
27
Dots & Lines
The Bottleneck
The answer is never about the big pipes. It is about the narrow place.
28
Dots & Lines
Matching People to Jobs
Greedy gets stuck. Then you fix it without starting over.
29
Dots & Lines
Coloring, and How Good Is Greedy?
Six clubs, two slots are enough, and greedy uses three. The order is to blame.
30
Logic & Proof
A Lower Bound
Two halves make an answer: a method that works, and a proof nothing beats it.
31
Ways of Counting
Rules That Look Back
To count a strip of ten, count a strip of nine and a strip of eight.
32
Ways of Counting
A Rule From a Table
Two patterns started together. One is always double the other, and you can see why.
33
Logic & Proof
Two Rules, One Answer
A formula and a count that disagree cannot both be right, so check.
34
Steps & Cost
Sorting Really Big Lists
At eight cards it hardly matters. At a thousand it decides whether the job is possible.
35
Steps & Cost
Which Method Would You Pay For?
The last real week. A decision, with money on it.
36
Steps & Cost
The Method Book, Finished
Thirty-three pages of methods, each with its price. This week it becomes one book.