These days, calculators on smartphones and watches have made much of the work of math disappear for many people, but the basic ability to think through an old-fashioned math puzzle can keep the brain sharp and help in everyday decisions. After all, knowing math means understanding how to spend and save money, and that’s something we all need.
To sharpen your wits, you can take on a puzzle that has had the whole internet, math nerds included, arguing over. It looks deceptively simple, a countdown from 9 to 3 on the left side. This downward progression on the left is accompanied by another series on the right that also descends in a pattern of some sort.
Yet, heated debates among math enthusiasts have centered around what the final answer is. Can you figure it out?
Some people have discovered a multiplication pattern on the left-hand side of the equation to solve the problem. The pattern is to multiply the number on the right by one less than itself x(x-1), which reliably produces the correct answer on the right side of the equation. For example, 9(8) = 72, 8(7) = 56, and so on. If we follow this rule all the way down to the bottom, we would get a final answer of 6 from the equation of 3(2) = 6.
So, is that the end of the whole debacle? Not quite; others have pointed out different patterns that result in entirely different answers.
Another way is to interpret the pattern on the right-hand side by looking at the sequential differences between each subsequent number: 72 – 56, then 56 – 42, then 42 – 30, etc., which results in a decreasing pattern of 16, then 14, then 12, etc. Each subsequent number decreases by 2. Then, we might expect the final answer to be 12.
But hold on! There is yet a third answer to this problem. Let’s take a look.
Some have recognized a pattern of decreasing multiplication on the left-hand side of the equation: 9 × 8, then 7 × 7, then 6 × 5, etc. Each subsequent number decreases by 1. If taken to its logical conclusion, this pattern results in an answer of 9 from the equation 3 × 3 = 9.
Yet, is it possible that one of these three answers is better than the rest? Some have argued that this is the case. They have also provided a logical explanation for why this is so.
Well, let’s first take a look at the first number in each equation and see if there is a pattern; there does seem to be a pattern, as each number in sequence decreases by 1, that is, except for the last line, which has a difference of 2. Yet, it might not be the case if we deduce that there is a missing line that begins with the number 4.
Now why is this missing line so important? Well, because logically, if we use any of the three patterns already demonstrated—whether it be x(x-1), decreasing subtraction, or decreasing multiplication—with the extra line starting with 4 included in the sequential pattern, we get the same answer in all three cases! And that answer is 6.
It is therefore logical to deduce that this missing line is part of the pattern for all three cases but is simply omitted, and that the best answer for this problem is indeed 6.
So, if you’re looking for a way to get the kids’ math skills sharp during the Holiday Season, you just might want to share it with them. Only don’t expect to get any consensus on the solution!