`person(1)` had to do `PROBLEMS`

through `START`

for homework last week.
`END``person(1)` had to do `PROBLEMS`

through `START`

for homework tonight.
`END``person(1)` was assigned `PROBLEMS`

through `START`

for homework last week.
`END``person(1)` was assigned `PROBLEMS`

through `START`

for homework tonight.
`END`

`person(1)` had to read `PROBLEMS`

through `START`

for homework last week.
`END``person(1)` had to read `PROBLEMS`

through `START`

for homework tonight.
`END``person(1)` was assigned `PROBLEMS`

through `START`

for homework last week.
`END``person(1)` was assigned `PROBLEMS`

through `START`

for homework tonight.
`END`

If `person( 1 )` did all of the `PROBLEMS` he was assigned, how many `PROBLEMS` did he do?
If `person( 1 )` read all of the `PROBLEMS` he was assigned, how many `PROBLEMS` did he read?

If `person( 1 )` did all of the `PROBLEMS` she was assigned, how many `PROBLEMS` did she do?
If `person( 1 )` read all of the `PROBLEMS` she was assigned, how many `PROBLEMS` did she read?

`ANSWER` `PROBLEMS`

Instead of counting `PROBLEMS`

through `START`

,
we can subtract `END`

from each number.
`START - 1`

Now the `PROBLEMS` are `1`

through

.`ANSWER`

So `person(1)` did `ANSWER``PROBLEMS`.

So `person(1)` read `ANSWER``PROBLEMS`.

Notice that he did

and not `ANSWER``ANSWER - 1``PROBLEMS`.
Notice that he read

and not `ANSWER``ANSWER - 1``PROBLEMS`.

Notice that she did

and not `ANSWER``ANSWER - 1``PROBLEMS`.
Notice that she read

and not `ANSWER``ANSWER - 1``PROBLEMS`.

A baker has a whole {baguette|loaf of bread}.

How many parallel cuts must {he|she} make to have exactly

even slices?
`NUM`

`NUM -1` cuts

One cut will make two slices, two cuts will make three slices, and so on.

Therefore, we need

cuts to make `NUM - 1`

slices.`NUM`

`person( 1 )` is building a straight fence, with posts one meter apart.

If the fence is

meters long, how many fence posts does he need?
`LENGTH`

If the fence is

meters long, how many fence posts does she need?
`LENGTH`

`LENGTH + 1` fence posts

If the fence is one meter long, he needs two posts (one for each end).

If the fence is one meter long, she needs two posts (one for each end).

If the fence is two meters long, then he needs three posts, and so on.

If the fence is two meters long, then she needs three posts, and so on.

Therefore, he needs

posts for a `LENGTH + 1`

meter fence.
`LENGTH`

Therefore, she needs

posts for a `LENGTH + 1`

meter fence.
`LENGTH`