randRange( 3, 5 ) randRange( 20, 50 ) randRange( 7, 15 ) START + ( NTH - 1 ) * INCR

person( 1 ) starts counting at START, and he counts by cardinalThrough20( INCR )s.

person( 1 ) starts counting at START, and she counts by cardinalThrough20( INCR )s.

If START is the 1st number that person( 1 ) counts. what is the NTHth number that he counts?

If START is the 1st number that person( 1 ) counts. what is the NTHth number that she counts?

ANSWER

What is the first number that he counts?

What is the first number that she counts?

`START`

What is the second number that he counts?

What is the second number that she counts?

`\begin{align*}&START + INCR \\ &= START + INCR\end{align*}`

What is the third number that he counts?

What is the third number that she counts?

`\begin{align*}&START + INCR + INCR \\ &= START + (2 \times INCR) \\ &= START + 2 * INCR\end{align*}`

What is the NTHth number that he counts?

What is the NTHth number that she counts?

`\begin{align*}&START + (NTH - 1\timesINCR) \\ &= START + ( NTH - 1 ) * INCR \\ &= ANSWER\end{align*}`

randRange( 5, 10 ) ( NUM * ( NUM - 1 ) ) / 2

There are NUM people in a room.

If everyone shakes everyone else's hand exactly once, how many handshakes occur?

ANSWER

Given NUM people, each person shakes the hands of NUM - 1 other people.

The following is almost the answer.

`NUM \times NUM - 1 = NUM * ( NUM - 1 )`

We have double counted the handshakes though, since person( 1 ) shaking person( 2 )'s hand is the same handshake as person( 2 ) shaking person( 1 )'s hand.

Therefore, the following is the correct answer.

`\dfrac{NUM \times NUM - 1}{2} = ANSWER`

randRangeUnique( 2, 6, 2 ) NUM_COLORS * NUM_POTS

person( 1 ) wants to give his friend a potted plant. At the local florist, the flowers come in NUM_COLORS colors, and there are NUM_POTS types of flower pots.

person( 1 ) wants to give her friend a potted plant. At the local florist, the flowers come in NUM_COLORS colors, and there are NUM_POTS types of flower pots.

If he can choose any flower and any pot, how many different potted plants can person( 1 ) buy?

If she can choose any flower and any pot, how many different potted plants can person( 1 ) buy?

ANSWER

If person( 1 ) decided on a flower color, how many different potted plant combinations are there?

He can choose one of NUM_POTS flower pots, and so there are NUM_POTS different potted plants possible (given that he already chose a flower color).

She can choose one of NUM_POTS flower pots, and so there are NUM_POTS different potted plants possible (given that she already chose a flower color).

Since there are NUM_COLORS flower colors, there are `NUM_COLORS \times NUM_POTS = ANSWER` possible potted plants.