Math CentralQuandaries & Queries


Question from Sariyah:

Of the positive integers between 1000 and 10000 that are divisible by 8, how many have a 5 in the hundreds place?

Hi Sariyah,

I can help get you started.

  1. If an integer between 1000 and 10000 then it is an integer of the form X5YZ where each of X, Y, and Z is a digit, but X can't be zero.

  2. If an integer has its hundreds, tens and units digits A, B, and C respectively then the integer is divisible by 8 if and only if $A \times 100 + B \times 10 + C$ is divisible by 8.

As an example of the second point 5643744 is divisible by 8 since 744 is divisible by 8 but 5643740 is not divisible by 8 since 740 is not divisible by 8.


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