Open Middle®
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?
758-291=467
648-291= 357 would be the perfect answer, where each digit is used only once, wouldn’t it?