3digit numbers that are multiples of 7 with individual digits that add to 7.

**qtpipi** · February 6th 2011, 11:07 AM

how can i find all the 3 digit numbers that are multiples of seven with individual digits that add to 7? I've been trying to figure this out using modular arithmetic, but I think I'm doing it wrong.

**Plato** · February 6th 2011, 11:24 AM

Originally Posted by qtpipi

how can i find all the 3 digit numbers that are multiples of seven with individual digits that add to 7?

Using the floor function $\left\lfloor {\dfrac{{999}}{7}} \right\rfloor - \left\lfloor {\dfrac{{99}}{7}} \right\rfloor$ .

Tell us why that works.

**qtpipi** · February 6th 2011, 11:34 AM

the floor function just gives us the number of 3 digit numbers that are multiples of 7. i need to find which of these multiples of 7 have individual digits that add to 7.

**Plato** · February 6th 2011, 11:55 AM

Originally Posted by qtpipi

the floor function just gives us the number of 3 digit numbers that are multiples of 7. i need to find which of these multiples of 7 have individual digits that add to 7.

Sorry, I read the question too quickly.

**qtpipi** · February 6th 2011, 05:49 PM

figured it out!

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3digit numbers that are multiples of 7 with individual digits that add to 7.

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