Complete the following pattern. 331, 343, what, 367.
What can we say about the pattern that we can see in these oval shapes? Well, firstly, it seems to be an increasing pattern. In other words, the numbers are getting larger from left to right. This means that the rule to our pattern is either an addition or a multiplication rule. And although we’ve only been given three numbers in our pattern, we can also see that they’re odd. So we can make a prediction that the missing number is likely to be an odd number. But how are we’re going to find the rule for the pattern? Because we don’t know the fourth number in our pattern, we can’t see how 343 changes. And we can’t identify a rule for changing our mystery number into 367. In fact, the only two numbers that we do have sitting next to each other are the first two. And we can use these to help find the rule for our pattern.
What do we do to 331 to take us to 343? Well, 331 has three hundreds, three tens, and one one. And 343 has three hundreds too. But it also has four tens and three ones. Let’s look at how these digits have changed. The ones digit has increased from one to three. And so we’ve added two ones. The tens digit has increased from three tens to four tens. So it’s increased by one lot of 10. And we can see there’s been no change in the hundreds digit. So we can say that, to get from the first number to the second number, we’ve added one ten and two ones. In other words, we’ve added 12.
Let’s add another lot of 12 to find our missing number. 343 has three ones. And if we add two ones to this, we have a number that has five ones. 343 has four tens. If we add one more ten, we now have five tens. And our hundreds digit, as we’ve said already, stays the same. We would expect our missing number to be 355. And if we add 12 to 355, we get the answer 367, which was the last number in our pattern. So we know that our missing number is correct. We looked very closely at the first two numbers. And we found that the rule was to add 12 each time. And by adding 12 to 343, we found our missing number.
The pattern altogether is 331, 343, 355, and 367. And the missing number, that’s the third number in our pattern, was 355.