Item 3.3.10.b.

Suppose you have 22 coins, including \(2k\) nickels, \(2j\) dimes, and \(2l\) quarters (so an even number of each of these three types of coins). The number of pennies you have will then be

\begin{equation*} 22 - 2k - 2j - 2l = 2(11-k-j-l)\text{.} \end{equation*}

But this says that the number of pennies is also even (it is 2 times an integer). Thus we have established the contrapositive of the statement, “If you have an odd number of pennies then you have an odd number of at least one other coin type.”

in-context