CREATIVITY - OUTSIDE, BOTH SIDES, MANY SIDES

Here is a classic puzzle that many of you have probably seen it before.

Figure 1 shows 9 dots evenly spaced. Draw 4 straight lines without lifting the pen off the paper to cross the nine dots. (Note: Please spend about 3 minutes trying that before scrolling down to see subsequent paragraphs.)

Some people may have tried like those methods shown in Figure 2, but in each case the 4 lines do not cross all 9 dots. It seems like 4 lines are not enough, and we need 5 lines.

The answer? Figure 3 shows an answer, and Figure 4 illustrates one probable reason that limits us from getting the answer, i.e., the assumption that we cannot draw the lines outside the self-imposed square boundary formed by the 9 dots, but the instruction does not mention that the lines cannot be outside this square.

What are other answers besides that shown in Figure 3??

Now, let’s look at another puzzle. There are two parts in this puzzle. Here is Part 1.

There are 12 balls, same size and shape. One of the balls is faulty and slightly heavier, but you cannot feel the difference with your hands. How do you use a balance (Figure 5) three times and identify the faulty and slightly heavier ball? (Note: Please spend about 5 minutes trying that before scrolling down to see subsequent paragraphs.)

Most people should be able to find an answer for that. Figure 6 shows one solution. To arrive at this solution, one needs to think creatively, visually and logically, and be able to use an appropriate graphical means to explain the solution – in this case, a flow chart or decision tree method.

Can you complete the missing portion of Figure 6?

What are other answers besides that shown in Figure 6?

Now, Part 2.

There are 12 balls, same size and shape. One of the balls is faulty and is either slightly lighter or slightly heavier, but you cannot feel the difference with your hands. How do you use a balance (Figure 5) three times and identify the faulty ball, and state whether it is slightly lighter or heavier? (Note: Please spend about 10 minutes trying that before scrolling down to see subsequent paragraphs.)

Is it possible to solve the puzzle by using the balance only three times? It seems like we need to use the balance four or more times. However, three times are enough. Figure 7 shows a solution. The left-hand portion of Figure 7 is not difficult to figure out, but the right-hand portion is relatively more complex. For the right-hand portion, as illustrated in Figure 7, the key strategy is to separate Balls 5, 6, 7, 8 with 5, 6, 7 in a group and 8 alone, and, similarly, separate Balls 9, 10, 11, 12 with 10, 11, 12 in a group and 9 alone (The ball numbers mentioned are arbitrary). Then swap Balls 8 and 9, i.e., put Balls 5, 6, 7, 9 on one side of the balance, and three ‘good’ balls’ (Balls 1, 2, 3 are used in the illustration) and 8 on the other side of the balance (See Figure 8 which is an extracted and enlarged part of Figure 7).

Can you complete the missing portion of Figure 7?

What are other answers besides that shown in Figure 7?

The solution illustrated by Figures 7 and 8 signifies an approach in creative thinking and creative problem solving, which is to “study both sides and swap components’’ if applicable and see if it works.

Normally, in problem solving, we tend to keep all components of groups together and do not try to separate components to explore potential solutions. However, sometimes, solutions may be possible by swapping components between two groups, and even exchanging components across three, four, five, or more groups.

Hence, it may be beneficial to explore separating and swapping components between systems or sub-systems in design (product, visual communication, interior, architecture, etc.), members between management teams or project teams, and so on.