Often we are faced with problems we do not know the answers to; however, we still have to find solutions. We use a strategy called Guess and Test or Trial and Error. We use this strategy on a daily basis without even realizing it. If you have a ring full of keys and you know one of them opens the front door, what do you do? You continue to try keys until one opens the front door. This is an example of Guess and Test. Try the problem below and see how well you Guess and Test.

Place the digits 1, 2, 3, 4, 5, and 6 in the circles so that the sum of the three numbers    

on each side of the triangle is 12. Try this first before you continue.

Each number must be used exactly one time when arranging the numbers in the triangle. The sum of the three numbers on each side must be 12

Tear off six pieces of paper, mark the numbers 1 through 6 on them, and then try combinations until one works.

Arrange the pieces of paper in the shape of an equilateral triangle and check sums. Keep rearranging until the three sums of 12 are found.

With 1, 2, 3 in the corners, the sums of the sides are two small; similarly with 1, 2, 4. Try 1, 2, 5 and 1, 2, 6. The side sums are still too small. Next try 2, 3, 4 then 2, 3, 5 and so on, until a solution is found. We also could begin with 4, 5, 6 in the corners then try 3, 4, 5, and so on.

Start by assuming that 1 must be in a corner and explore the consequences.

If 1 is placed in a corner, we must find two pairs from the remaining five numbers whose sum is 11. However, out of 2, 3, 4, 5, and 6, only 6 +5 = 11. Therefore, we conclude that 1 cannot be in a corner. If 2 is in a corner, there must be two pairs left that add to 10. But only 6 + 4 = 10. Therefore, 2 cannot be in a corner. Finally, suppose that 3 is in a corner. Then, there must be two pairs left that add to 9. However, only 5 + 4 = 9 among the remaining numbers. Thus, if there is a solution 4, 5, and 6 will have to be in the corners. By placing 1 between 5 and 6, 2 between 4 and 5, and 3 between 4 and 5, we obtain a solution.

Notice how we have solved this problem in three different ways using Guess and Test. Random Guess and Test is often used to get started, but it is easy to lose track of the various trails. Systematic Guess and Test is better because you develop a scheme to ensure that you have tested all possibilities. Generally, Inferential Guess and Test is superior to both of the previous methods because it usually saves time and provides more information regarding possible solutions

The Guess and Test strategy may be appropriate when:

• There is a limited number of possible answers to test

• You want to gain a better understanding of the problem