### Target Practice Plus

“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 a long trek.

1. Make 180 from the set {1, 5, 8, 20, 25, 50}. Look for a second solution.
2. Make 109 from {2, 7, 10, 12, 25, 50}. Can you succeed using four or fewer numbers?
3. Make 289 from {2, 5, 7, 13, 25, 50}. For this one, I found many solutions using six and five, but I don’t know if 289 can be made from just four of the set.

solutions