Four digits are shown in the grid. Part a) Write down the largest odd number possible by arranging these digits. You may only use each digit once.
Okay, so the question asked us to write down the largest odd number possible by arranging the digits, which means we’re not going to be adding or multiplying these numbers together, just arranging them in order. There are four digits, so four spaces that we need to fill in our number.
Now, to make this number as large as possible, we won’t be including a decimal point. So this means that the first digit in our number will represent thousands, the second digit will represent hundreds, the next digit will represent tens, and the final digit will represent units.
We’re told that the number needs to be an odd number. Now, for a number to be an odd number, this means that its final digit, the digit in the units column, must also be an odd number. The only one of the four digits which is an odd number is the number three. So this must go in the units column.
Next, we want to make this number as large as possible, which means we need the largest possible number of thousands. The largest number in the grid is the eight. So we’ll put this in the thousands column. Next, we want the largest possible number of hundreds. So the largest number left in our grid is six, which we’ll put in the hundreds column. The only number left is two. So we need to put this two in the tens column.
The largest odd number possible by arranging these digits is 8623. It’s just worth pointing out that this isn’t in fact the largest number possible by arranging these digits. That would be 8632. But as we were asked for the largest odd number, we needed the three in the units column rather than the two. So this is the largest possible odd number.
Part b says, “State all the possible two-digit numbers you can make with these four digits. You may only use each digit once per number. ”
So this time, we’re only looking to use two of the numbers at a time to create two-digit numbers. We need to take a systematic approach. So let’s start by listing all of the two-digit numbers that begin with eight. We can have a three for the second digit making 83 or six making 86 or two making 82. Remember we can only use each digit once per number. So the number 88 is not an option.
Next, let’s consider all of the two-digit numbers starting with a three. The second digit could be an eight, a six, or a two. So we have the possibilities 38, 36, 32. We can then list all of the possible two-digit numbers beginning with six. So we have 68, 63, and 62 and finally all of the two-digit numbers beginning with two: 28, 23, and 26.
We have three rows and four columns. So we have 12 possibilities in total. And this is the full list of all the possible two-digit numbers we can make with these four digits, using each digit only once per number.