Complete the table below by following the pattern.
So what can we see in front of us? We have a three-by-three table containing some numbers. We’ve got a complete top row. Well, if you want to think about columns, we’ve got a complete first column too. There are also three missing numbers. And we’re asked to complete the table. We’re asked to do so by following the pattern. Now, where’s the pattern in this table? Is there a pattern working across each row from left to right? Or is there a pattern going down each column from top to bottom? Let’s look at the numbers that we do know in the table. We’ll see if we can find any patterns.
First of all, is there a pattern working across each row? The only full row that we’ve got to look at is the top one. And the first thing that we notice about these three numbers is that they all have the same number of ones. They all end in a three. So when we look at how each number changes, we only need to look at the hundreds and the tens digits. Our first number has digits that show 380, which is the same as 38 tens. And then, we have 42 tens and then, finally, 46 tens. How are these numbers increasing each time? Well, they’re getting larger by four tens. In other words, we’re adding 40.
383 add 40 is 423, and then 423 add 40 is 463. Now, we could use this pattern of adding 40 across each row to help us find our missing numbers. But there’s also another way we could use to find the answer. And it’s worth just mentioning this before we carry on. The only full column that we can look at is the first one. But if we look at the numbers going down that column, we can see a pattern there as well. The first thing that we notice about these numbers is that they all have the same number of tens and ones. They all end in 83. And so, when we’re looking for a pattern, we can ignore the tens and the ones. And we just need to look at the hundreds and thousands digits. How do the hundreds and thousands digits change in these numbers?
Well, firstly, we can see that the hundreds digit increases by one each time. We can see 300 in the first number then 400 then 500. And the thousands digit increases by four. There’s no digit in the thousands column in the first number. And then, we have 4000 and finally 8000. So the pattern of numbers going down the column is that we add 4100 each time. So we found a pattern going across the table and a pattern going down the table. And we can choose whichever pattern we like to complete the table with our missing numbers.
Let’s use our plus-40 pattern to find the first missing number. We’ll start with 4483. And then, we’re going to add four tens, 4483, 4493, 4503, 4513, and then finally 4523. If you want to check that this is a correct answer, we can always look down from 423 and see whether we’ve added 4100. That’s our other pattern, isn’t it? Now, it’s a little bit easier to add 40 to this number because we don’t have to cross into the next 100. 4523 plus 40 is going to be 4563.
Notice how the last two digits of our numbers are the same. Our first number ended in 23, just like the number above. And our second number ended in 63, just like the number above. So we can predict that our third missing number is going to end in 23. Let’s count on four tens from 8583, 8593, 8603, 8613, 8623. There are lots of patterns that we can find in this table. And we can use them to find the three missing numbers. Our three missing numbers, as we look through the grid from left to right and from top to bottom, are 4523, 4563, and 8623.