These are the answers to the insight problems listed in Box 8.3 on pages 165-166 of Good Thinking.

1. Click here for the answer.

2. I've numbered the circles to make this solution easier to see:

0 6 1 2 9

1 2 3 4 5

3 4 5 7 8

6 7 8 9 0

So 6 and 9 moved up to the second line, and 0 moved to the bottom.

3. $30. He invested $60 in the horse, and ended up with $90 when all the trading was done.

4. Here's how: We start with four chains with 3 links each.

OOO OOO OOO OOO

We open each of the links in the first set so it looks like this:

-- -- -- OOO OOO OOO

That cost us 6 cents, 2 cents to pry open each of the 3 links.

Now we use the open links to connect the remaining segments together, like this:

OOO--OOO--OOO--

We close all of the links, looping the last one back to attach the last O and the first O together. That costs us 9 cents, 3 cents to close each of the 3 links. 6+9=15 cents.

5. The easiest way is to divide the garden into four circles, like this:

OO

OO

Then plant each tree in the exact middle of each circle.

6. They are both equally contaminated. Think of it this way:

Start: Bowl A has 2 t oil; Bowl B has 2 t vinegar

Step 1: Bowl A has 1 t oil; Bowl B has 2 t vinegar + 1 t oil

Step 2: Bowl A has 1.5 t oil + 1 t vinegar; Bowl B has 1 t vinegar + 1.5 t oil

1. Click here for the answer.

2. I've numbered the circles to make this solution easier to see:

0 6 1 2 9

1 2 3 4 5

3 4 5 7 8

6 7 8 9 0

So 6 and 9 moved up to the second line, and 0 moved to the bottom.

3. $30. He invested $60 in the horse, and ended up with $90 when all the trading was done.

4. Here's how: We start with four chains with 3 links each.

OOO OOO OOO OOO

We open each of the links in the first set so it looks like this:

-- -- -- OOO OOO OOO

That cost us 6 cents, 2 cents to pry open each of the 3 links.

Now we use the open links to connect the remaining segments together, like this:

OOO--OOO--OOO--

We close all of the links, looping the last one back to attach the last O and the first O together. That costs us 9 cents, 3 cents to close each of the 3 links. 6+9=15 cents.

5. The easiest way is to divide the garden into four circles, like this:

OO

OO

Then plant each tree in the exact middle of each circle.

6. They are both equally contaminated. Think of it this way:

Start: Bowl A has 2 t oil; Bowl B has 2 t vinegar

Step 1: Bowl A has 1 t oil; Bowl B has 2 t vinegar + 1 t oil

Step 2: Bowl A has 1.5 t oil + 1 t vinegar; Bowl B has 1 t vinegar + 1.5 t oil

7. How to draw the figure without lifting your pencil from the paper. Start where the gap is shown on the top line, move your pencil to the left all the way around to the same place. Then follow the path down and change direction when you reach the gaps.

8. The trick is to let the pens overlap so that some of the animals are in two pens. Here is one solution.

9. This is one way to divide the figure into four equal parts.

10. Here is one way to arrange 10 pennies so that you have five rows (lines) of four pennies in each row. The rows are horizontal and slanted.