person( 1 ) starts counting at START, and he( 1 ) counts by cardinal( INCR )s.
If START is the 1st number that person( 1 ) counts. what is the NTHth number that he( 1 ) counts?
ANSWER
What is the first number that he( 1 ) counts?
START
What is the second number that he( 1 ) counts?
\begin{align*}&START + INCR \\
&= START + INCR\end{align*}
What is the third number that he( 1 ) counts?
\begin{align*}&START + INCR + INCR \\
&= START + (2 \times INCR) \\
&= START + 2 * INCR\end{align*}
What is the NTHth number that he( 1 ) counts?
\begin{align*}&START + (NTH - 1\timesINCR) \\
&= START + ( NTH - 1 ) * INCR \\
&= ANSWER\end{align*}
There are NUM people in a room.
If everyone shakes everyone else's hand exactly once, how many handshakes occurred?
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
person( 1 ) wants to give his( 1 ) 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( 1 ) 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( 1 ) can choose one of NUM_POTS flower pots, and so there are NUM_POTS different potted plants possible (given that he( 1 ) already chose a flower color).
Since there are NUM_COLORS flower colors, there are NUM_COLORS \times NUM_POTS = ANSWER
possible potted plants.