Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make two different pairs of three-digit numbers that form a true number sentence. You may reuse all the digits each difference.

### Hint

How can we determine which digits would be poor choices to place?

### Answer

There are many possible answers including 874 – 291 = 583 and 587 – 291 = 296. To be clear, the 291 in the number being subtracted to not count as being used.

Source: Robert Kaplinsky

I am working on this with my students right now and they were curious why you decided to subtract 291 of all the 3 digit numbers. Thanks!

Gosh, that’s a great question. I’m trying to remember why I picked that number. I know that some numbers would be trivial. For example subtracting 100 would not even be interesting. I think I wanted to do something that would almost certainly require there to be some kind of borrowing or regrouping.

I am confused also about 874-291=583. Because the first direction says use 1 to 9 at most one time each, but 8 is used twice here.

354 – 291 = 352

543 – 291 = 352

Hi! I love Open Middle. Thank you for inspiring so much critical math thinking. I feel like I don’t fully understand the answer example. Why can the digit 8 be used twice in 874 – 291 = 583?