 Directions: Daniel was making chocolate cookies. He had _ _ cookies in each row and _ _ many rows. There were a total of 84 cookies. How many cookies were there in each row and how many rows of cookies were there? Draw a model to support your answer.

You may use the digits 0-9 once in any of the blank boxes. (The answer of 84 does not eliminate the 8 or the 4.)

### Hint

How many ways can you make 84?

There are multiple answers due to the factors that make 84.
12 x 07 = 84
06 x 14 = 84
04 x 21 = 84
02 x 42 = 84

Source: Daniel Rocha

## Make The Time

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. Nice question Daniel.
Should the directions be changed from “You may use the numbers 0-9” to “You may use the digits 0-9”?

• I don’t like it you should have to fill in the blanks to look at the answer

• This app sucks cuz you can’t fill in the blanks

• You can just do it on paper, dude.

2. “You may use the numbers 0-9 once in any of the blank boxes. (The answer of 84 does not eliminate the 8 or the 4.)”

My class just worked through this Open Middle problem. We noticed that you included 02 x 42 as a possible answer. We read the directions as meaning that we could only use 0-9 once in the equation. Did we read too deeply into it? Also, do 01 x 84 work and 03 x 28 work?

Thank you so much!

• I agree. 02 x 42 should not be included as an answer that fits the clues.
We also came up with 03 x 28 by working with 3, 4, and 7.

3. Where’s the student worksheet with the boxes?

• This is the second problem I’ve seen on this website, and both have “trick” solutions using nonstandard notation. I think putting such an emphasis on trick questions is counter-productive. There are plenty of problems to pose that are _tricky_ but not _tricks_, that rely on deep mathematical reasoning not playing games with superficial notation.

• There isn’t any boxes

• • 14 x 6 = 84
84 x 1 = 84
21 x 4 = 84
esa es mi respuesta de la materia✌😎✌

4. 4 rows of 21 = 84.

• You will never know

5. 2 x 42= 84
4 x 21= 84
7 x 12= 84
6 x 14= 84

6. Is there a new google sheet for this week?

7. Why did you not eliminate the 4 and 8 to make it hard for us.

8. Why did you not eliminate the 4 and 8 to make it hard for us its to easy.

9. 10. i agree with Ayesha 7 rows and 12 c cookies each

• Me too. 7 rows of 12 cookies each.

11. 12. Scarlett Salaz

12X7=84

13. Zoe Savvoulides

84 X 01= 84

14. 15. 16. 17. 12 x 07 = 84
06 x 14 = 84
04 x 21 = 84
02 x 42 = 84

18. 19. 