### Target Practice Plus #16

“Uncle Bob”

Here’s a new twist on a familiar activity: using simple arithmetic, construct a target number from a given set of numbers. For example, let’s construct 135 from the set

{2, 3, 4, 15, 50, 100}

We must use only the four operations: addition, subtraction, multiplication, and/or division. Numbers in the set can be used only once in the solution. One solution is

(2 + 3 + 4) x 15 = 135

You can see that using grouping symbols is also permitted, or in other words, the final result can be made from preliminary ones, as in

2 + 3 + 4 = 9
9 x 15 = 135.

Here’s the twist. The solution above uses four of the six given numbers. Can we find a more concise solution? I find that this activity requires me to be creative and flexible in my thinking. We'd like a second solution, if it exists, to use fewer than four members of the set. I found one using three numbers, and you may have too:

100 + 50 – 15 = 135

Try these three challenges. I rank them as easy, medium, and hard in difficulty.

1. Make 316 from {2, 8, 18, 34, 50, 100}. There are solutions using five or four of the numbers. Find a solution using all six.

2. Make 192 from {2, 3, 5, 9, 13, 17}. There are solutions using five or four of the numbers. Find a solution using all six.

3. Make 16 from {3, 9, 17, 35, 85, 150}. One solution uses five of the set. Can you solve it with just three?

solutions