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What is the largest nine-digit number that can be formed using all the digits of six, six, seven, nine, seven, five, zero, one, and three?
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As part of the question, we’re given nine digits.
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Those nine digits we’ve just read out.
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And we need to rearrange those digits so that they make the largest possible nine-digit number.
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Now, we know that the value of a digit in a number depends on where we write it.
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For example, the digit three might have a value of three tens or three thousands, maybe even three millions.
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It depends where we write it in the number.
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So, perhaps the first thing we should do is to draw a place value grid to think about what the value of each digit in a nine-digit number is going to be.
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We can think of our digits in groups of three.
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So, going from right to left, we could call our first group of three the ones.
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And we have the ones, tens, and hundreds digits.
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Our second group of three are our thousands.
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Here, we have the thousands digit, ten thousands digit, and hundred thousands digit.
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Our final group of three are our millions.
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We have the millions, tens of millions, and hundred millions digits.
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Let’s start by thinking about the hundred millions place.
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If we want to make a digit that’s the largest possible nine-digit number, which digit do we want to put in the hundred millions place?
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This is the place with the largest value.
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Well, there’s no point putting a one in there because there are other digits that are greater.
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We could even do better than a three or a five.
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Instead of just going through each digit, we can say to ourselves that we just need to pick the largest possible digit.
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And if we look at our list of digits, the largest possible digit is nine.
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So, the largest possible number will have nine hundred millions.
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It can sometimes be tricky to spot which digits we’ve used and which we haven’t.
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So, what we’ll do is we’ll write them out underneath and we’ll rub them out as we use each one.
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So, to begin with, we’ve used the digit nine.
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The next place with the greatest value is the ten millions place.
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And again, to make this number have the largest possible value, we need to pick the next largest digit.
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We’ve used the digit nine, so the digit with the next largest value is seven.
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So, let’s cross off seven from our list.
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And there’s another seven in our list, so we can put this in the millions place.
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What we’re doing really is putting the digits in order from largest to smallest.
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This is going to give us the largest possible nine-digit number.
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The next largest digits are two sixes.
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And we can put these in the hundred thousands and ten thousands places.
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In our thousands place, we need to put the digit five.
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And then, we’re left with a digit zero, one, and three.
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And if we put these in order from largest to smallest, we get 310.
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We’ve found the answer by rearranging the digits from largest to smallest so that the largest digit has the largest possible value and the smallest digit has the smallest possible value.
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So, the largest nine-digit number that we can make using the digits six, six, seven, nine, seven, five, zero, one, three is 977665310.