Yesterday, I was asked to answer this Fifth Grade (Primary Five) math question. See if you can obtain the answer without having to build the table.
For those of you who freak out even at the hint of a math question, please note that this is NOT really a math problem (it is just disguised as one). It is designed to test your thinking abilities, and as leaders, we must be able to at least address questions like this. If we are afraid to tackle seemingly math-based questions, we will have a hard time leading our team to solve similar questions. So for now, get past the math-ness of this question and come up with your answer.
Did you get Column A? Well done! That is the answer!
If you didn't get that answer, go back and try to figure it out.
Okay, good. Now let's extend this a little bit more. Which column would the number "1566" appear?
The correct answer is C.
Did you get that too? If yes, then you are smarter than a fifth grader.
The number one key leadership skill for 2020 is complex problem solving as identified by the World Economic Forum. The thinking process for complex problem solving starts with structured problem solving, which this question is. Hence, if we want to build complex problem solving skills, we must be able to build structured problem solving skills. In this article, if you are not already adept at it, I will help you uncover your own structured problem solving skills, and from there, lead in into complex problem solving (which we will not dive into today). I hope this will dispel all notions that you are bad at math, and you can't solve math-based problems. Math is just the proxy for logical thinking, and that is a key trait for problem solvers.
1. Identify determinants
The first thing you need to do in any problem-solving process is to identify the determinants. A determinant is basically a factor which directly impacts the outcome of a problem. In our math problem, the determinants are consecutive natural numbers, although the order with which they appear on our grid may not be conventional.
Let's now take a practical problem.
You are the manager in the management office of a new condominium project that has been receiving numerous complaints about the speed of the elevators. Apparently, it is moving too slowly, and people have to wait many minutes for the arrival of the lift. The lift engineers say that this is the nature of this model of lift, and they cannot increase its speed. What can you, as the manager in the management office, do?
So, what are the determinants of this problem? Lift speed, surely; waiting time, surely; what about boredom? What about distraction? What about time of day?
Notice that each of these determinants allows us to reframe the situation differently. This is something we will go into shortly.
2. Identify patterns
One of the key issues with structured problem solving, such as the math question above, is that there is a pattern. Many complex problems also involve patterns, but these are likely the confluence of different patterns coming together to make it more difficult to predict what the next iteration is (though not impossible). In these less complex, structured problems, the key to finding your solution is to find the pattern.
In the case of the math question, we see the numbers moving from Column A to Column D and then back from Column D to Column A. And this is repeated... Hence, A to D, D to A. A to D, D to A; the cycle repeats every 8 numbers. Contrast this sequence with this other one...
This is considerably more complex, though still predictable. If you notice, the pattern of A to D increases with each new row. So Row 1 is only A to D; then Rows 2 and 3 form A to D, then D to A. This increases for Rows 4, 5 and 6, which goes from A to D, D to A, then A to D again; and then Rows 7 to 10 go from A to D, D to A, A to D then D to A. We can predict that the next set comprises five rows. from Row 11 to 15, starting A to D, D to A, then A to D, D to A and a last A to D. You will see this being repeated over more lines.
So pattern is the next key element in solving a problem, and let us now go back to the elevator problem, and see if there is a problem.
Well, let's assume that as you look into the complaints, you realise that all of them come in either in the mornings, or in the evenings. In fact, there is a time line; most of complaints fall into the 730am - 830am timing, and then 645pm to 730pm timing. This coincides with the time people go to work, and the time people come back from work. Monday to Friday. Interestingly, there are no complaints during the weekends. Not a single one. So you have established a pattern.
3. Formulate your hypothesis
Now that you have identified your pattern, you will be able to formulate a hypothesis, or in the case of a mathematical problem, an algorithm. This is a formula for finding the solution, given different determinants. So, what is the algorithm for our original math problem? We know that the pattern repeats every 8 numbers. So, if the number in question, 600, is divisible by 8, it means that it has fully filled all the sets of 8 above it without any remainder.
So, is 600 divisible by 8 (in other words, is 8 a factor of 600; or is 600 a multiple of 8)? The answer is yes! 600 divided by 8 is 75. Hence, it took 75 sets of 8 numbers to be filled until it got to 600. And this means that the number will be at Column A.
But what if the number is NOT divisible by 8? What does that mean? How can we tell which column the solution lies in? Well, that obviously means that the remainder is a key determinant in our solution. And indeed it is. So, if the remainder is 0, then the answer will be Column A. If the remainder is 1, it will also be Column A (since it starts again at A); if 2, then it will be Column B, 3 will be C, 4 is D, 5 again D, 6 is C, 7 is B. And this is our hypothesis (more precisely, our algorithm).
Of course a mathematical solution is much easier to determine. Let us see the lift problem. What is the hypothesis? Of course we know that these are working people from the timing of the complaints; we also know that waiting makes them impatient, and most of the complaints stem from this impatience. We also know that we cannot change the lift speed, so if a solution must come from reducing impatience. Or make the wait more enjoyable. After all, we are all aware that time flies when we are having fun! The key is to distract the residents such that they do not think about how slow the lift is. This is our hypothesis - that residents would not complain about the slowness of the lift if they are sufficiently distracted from it.
4. Test your hypothesis
The key to note about a hypothesis is that it might apply to a specific set of conditions, but it might not to another. Hence, 600 appearing at Column A might be a fluke. (We know that it isn't but hey, let's work the process here!) We need to test the remainder hypothesis. So we know for a fact that the number 14 lies in Column C. So, let's apply our hypothesis and see if we can indeed get that answer.
So dividing 14 by 8, returns a remainder of 6. Going back up to our "table of remainders" a remainder of 6 is indeed Column C. Cool! Need to test again. Let's build the original table to the 10th Row as such...
Now, let's take 29 and see where that should lie using our remainder theory. So 29 divided by 8 is 3 remainder 5. So, a remainder of 5 is Column D from above, which is corroborated by the table. Hence, we can say that the hypothesis works!
How does this translate with our lift problem? Well, the hypothesis is that a distracted person would not find the wait too long. So we will have to test it.
We could (barring cost issues for now)...
(1) place a mirror at each lift lobby and place a placard which asks "Are you dressed to impress?" or
(2) put up a video screen at each lift lobby and screen positive, inspiring and uplifting videos, or
(3) have a localised Pokemon Go in each lift lobby
You don't have to do all of them, of course; just pick one and see if it works to reduce the number of complaints. You also don't have to roll out the solution throughout the building just yet, simply apply it to a few test sites. This allows you to keep your failure costs down, and to also manage variables. If one does not work out, try another. We might need to completely exhaust all our options to conclusively eliminate the hypothesis (meaning, to say that the hypothesis does not work). When that happens, we will need to move onto a new hypothesis, and test that out again.
5. Use the hypothesis
Finally, once the hypothesis has been verified, you can roll out the solution. So, for the "600" position, all we do is divide 600 by 8, and the remainder is zero, telling us that it lies in Column A. In fact we can take any number and tell which column it lies in. Remember 1566? Let's see, 1566 divided by 8 is 195 remainder 6. A remainder 6 places it at Column C, as we mentioned earlier. And maybe let's go whole hog now...what about 7,223,852? Well, dividing 7,223,852 by 8 gives a remainder of 4, and that put it in Column D!
And for the lift issue? Provided that we have confirmed the hypothesis, and found that all the 3 options will distract the residents, then we should go with the option that provides us with the best outcome, balanced with the cost of the solution. And this happens to be the mirror option. Only a one-time cost with no additional recurring costs.
The definitive skill for 2020
So, are YOU smarter than a 5th Grader? I'll bet you are now; and I'll bet you don't recoil at the sight of a math question as much as you did. By being able to break down the problem into its determinants, identifying patterns, creating hypotheses, testing the hypotheses, and then using them, you can solve any 5th Grade Problem Question.
But wait! You can solve any structured problem out there too! And that makes you way smarter than a Fifth Grader. So don't be afraid of problems; cherish them. Because they allow us to stretch our thinking, question our assumptions, build new hypotheses, test them and apply them.
Now that is the definitive skill for 2020!
Advance your employability through to 2020
The World Economic Forum identified the Top 10 skills for 2020 and complex problem solving lies at the top! Download this infographic and share it with your HR department, your boss, and focus your own development along these lines. It will not only keep you employable in 2020, but even advance your career well past the next decade!
It all starts with this one click...