Ch1 Challenge Problem

What is the sum of the first sixty-one positive integers?

“Echoing” a one-digit number to make it a two-digit number (for example, making 2 into 22) is equivalent to multiplying by eleven. Echoing a two-digit number to make it a four-digit number (for example, making 23 into 2323) is equivalent to multiplying the two-digit number by what value?

Given numbers a and b, let a@b equal 2a + 2b. For example, 3@4 equals 14.

Show that @ is commutative.

Given numbers a and b, let a@b equal 2a + 2b. For example, 3@4 equals 14.

Show that @ is not associative.