Let's discuss a problem from the AMC 2022 Middle Primary Category: Problem 28 which revolves around puzzle.

Question

On a digital display, a combination of bars light up to represent each digit as shown:

In some special numbers, the number of bars which light up in the digits is the same as the sum of the digits. For example, in 373 the number of bars is (5+3+5=13) which is the equal to (3+7+3=13). What is the largest such three-digit number?

Solution

We have to find the largest three digit number who satisfies this condition.

The largest single digit number is $9$. If we find the number of bars included in it then it will be $6$. Digit $9$ has $6$ bars in it. So to make it most largest for the 2nd digit as well we will consider the digit $9$. It is also having $6$ bars. Thus digit $99$ is having $12$ bars. But if we add $9+9$ we get $18$. Thus we are still $6$ bars behind. $0$ is the digit having $6$ bars there. Thus if we consider the largest number to be $990$ and if we add the number of bars we are using that is = $6+6+6 = 18$. Also the digit sum is $9 + 9 + 0 = 18$.

Thus the largest number to be $990$.

What is AMC (Australian Mathematics Competition)?

The Australian Mathematics Competition (AMC) is one of Australia's largest and oldest annual mathematics competitions, aimed at fostering interest and excellence in mathematics among students.

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