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Directions: Old Mother Hubbard is baking cookies so her cupboards won’t be bare anymore! She bakes 109 cookies in all. She bakes the cookies on 4 cookie sheets. Each cookie sheet is arranged into equal rows and columns, but not every cookie sheet has the same number of rows and columns.

Using digits 0-9, at most once, how might the cookies be arranged on the cookie sheets?
(_ x _) + (_ x _) + (_ x _) + (_ x _) = 109

Hint

Since you’re only using 8 of the digits 0-9, which might you not use? What are the possible combinations of factors that could be used on each cookie sheet? What are the possible combinations of products that could add to 109? How can you organize your trials to eliminate repeating the same combination?

Answer

Answer 1: ( 6 x 8)+ (7 x 4) + (3 x 5) + (9 x 2) = 109
Answer 2: (4 x 8) + (7 x 2) + (3 x 6) + (9 x 5 )= 109
** There are probably more correct answers.

Source: Linda Hutcheson

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Directions: Using the numbers 1-9, each one time only, fill in the blanks to make …

26 comments

  1. 9×8=72
    7×3=21
    5×2=10
    1×6=6
    72+21+10+6=109 😀

  2. (4×3)+(7×2)+(3×6)+(9×2)=109

  3. (6×8)+(7×4)+(3×5)+(9×2)=109

  4. Danitza Marenco

    (6×8)+(7×4)+(3×5)+(9×2)=109 is what i got

  5. 9×5+3×8+4×7+2×6=109

  6. 5×5, 5×5, 4×7, 4×7,

  7. (7X5)+(6X6)+(8X3)+(2X7)=109
    THIS IS MY ANSWER

  8. 4×9 5×8 7×3 6×2 is 109.

  9. 6X8=48 9X2=18 7X4=28 3X5=15 total is 109

    48+18+28+15=109

  10. 5×8 + 7×3 + 4×9 x 6×2=109

  11. (7×5)(6×6)(8×3)(2×7)=109

  12. Scarlett Salaz

    6X8=48 9X2=18 7X4=28 3X5=15 total is 109

    48+18+28+15=109

  13. (5*9)+(3*8)+(3*5) + (5*5)=109
    45+24+15+25=109

  14. (6 x 8= 52)
    (7 x 5= 35)
    (5 x 2= 10)
    (4 x 3= 12)

    52+35+10+12=109

  15. (4 x 8) + (7 x 2) + (3 x 6) + (9 x 5 )= 109

  16. Answer 1: ( 6 x 8)+ (7 x 4) + (3 x 5) + (9 x 2) = 109

  17. Answer 1: ( 6 x 8)+ (7 x 4) + (3 x 5) + (9 x 2) = 109 is this it

  18. (6 x 8)+ (7 x 8)+ (3+5)+ (9 x 2) = 109

  19. (9 x 7) + (8 x 5) + (6 x 1) + (0 x 2) = 109

  20. 7×2=14
    3×6=18
    4×8=32
    9×5=45
    90+10=100+9=109

  21. (9×8)+(7+5)+(2×1)+(0x6)=109

  22. (4×8)+(7×2)+(3×6)+(9×5)=109

  23. (6×9) + (5×7) + (3×4) + (1×8)

  24. Rudolf Österreicher

    Here are all the 44 unique solutions (except for swapping cookie sheets around or swapping rows and columns):
    (0 * 1) + (2 * 3) + (5 * 8) + (7 * 9) = 109
    (0 * 1) + (2 * 4) + (5 * 9) + (7 * 8) = 109
    (0 * 1) + (2 * 8) + (5 * 6) + (7 * 9) = 109
    (0 * 1) + (3 * 9) + (5 * 8) + (6 * 7) = 109
    (0 * 2) + (1 * 6) + (5 * 8) + (7 * 9) = 109 Susans solution
    (0 * 2) + (1 * 7) + (5 * 6) + (8 * 9) = 109
    (0 * 2) + (3 * 9) + (5 * 8) + (6 * 7) = 109
    (0 * 3) + (1 * 2) + (5 * 7) + (8 * 9) = 109
    (0 * 3) + (1 * 6) + (5 * 8) + (7 * 9) = 109
    (0 * 3) + (1 * 7) + (5 * 6) + (8 * 9) = 109
    (0 * 3) + (2 * 4) + (5 * 9) + (7 * 8) = 109
    (0 * 3) + (2 * 8) + (5 * 6) + (7 * 9) = 109
    (0 * 4) + (1 * 2) + (5 * 7) + (8 * 9) = 109
    (0 * 4) + (1 * 6) + (5 * 8) + (7 * 9) = 109
    (0 * 4) + (1 * 7) + (5 * 6) + (8 * 9) = 109
    (0 * 4) + (2 * 3) + (5 * 8) + (7 * 9) = 109
    (0 * 4) + (2 * 8) + (5 * 6) + (7 * 9) = 109
    (0 * 4) + (3 * 9) + (5 * 8) + (6 * 7) = 109
    (0 * 6) + (1 * 2) + (5 * 7) + (8 * 9) = 109 <– Melissas solution
    (0 * 6) + (2 * 3) + (5 * 8) + (7 * 9) = 109
    (0 * 6) + (2 * 4) + (5 * 9) + (7 * 8) = 109
    (1 * 2) + (3 * 5) + (4 * 9) + (7 * 8) = 109
    (1 * 2) + (3 * 7) + (4 * 8) + (6 * 9) = 109
    (1 * 2) + (3 * 8) + (4 * 5) + (7 * 9) = 109
    (1 * 2) + (3 * 9) + (4 * 6) + (7 * 8) = 109
    (1 * 3) + (2 * 5) + (4 * 6) + (8 * 9) = 109
    (1 * 3) + (2 * 7) + (4 * 5) + (8 * 9) = 109
    (1 * 4) + (2 * 6) + (3 * 7) + (8 * 9) = 109
    (1 * 4) + (2 * 8) + (5 * 7) + (6 * 9) = 109
    (1 * 5) + (2 * 6) + (4 * 9) + (7 * 8) = 109
    (1 * 5) + (2 * 7) + (3 * 6) + (8 * 9) = 109
    (1 * 6) + (2 * 5) + (3 * 7) + (8 * 9) = 109
    (1 * 6) + (3 * 9) + (4 * 5) + (7 * 8) = 109
    (1 * 7) + (2 * 3) + (4 * 6) + (8 * 9) = 109
    (1 * 7) + (2 * 4) + (5 * 8) + (6 * 9) = 109
    (1 * 8) + (2 * 4) + (5 * 6) + (7 * 9) = 109
    (1 * 8) + (3 * 4) + (5 * 7) + (6 * 9) = 109
    (1 * 8) + (3 * 6) + (4 * 5) + (7 * 9) = 109
    (2 * 6) + (3 * 7) + (4 * 9) + (5 * 8) = 109
    (2 * 6) + (3 * 8) + (4 * 7) + (5 * 9) = 109
    (2 * 7) + (3 * 6) + (4 * 8) + (5 * 9) = 109
    (2 * 7) + (3 * 9) + (4 * 5) + (6 * 8) = 109
    (2 * 8) + (3 * 5) + (4 * 9) + (6 * 7) = 109
    (2 * 9) + (3 * 5) + (4 * 7) + (6 * 8) = 109

    But having 0 rows or columns is a bit strange: Old Mother Hubbard would only really use 3 cookie sheets instead of 4. And it would be strange to say that one of her cookie sheets has, for example, 0 rows and 4 columns.

    So we're really left with these 23 solutions:
    (1 * 2) + (3 * 5) + (4 * 9) + (7 * 8) = 109
    (1 * 2) + (3 * 7) + (4 * 8) + (6 * 9) = 109
    (1 * 2) + (3 * 8) + (4 * 5) + (7 * 9) = 109
    (1 * 2) + (3 * 9) + (4 * 6) + (7 * 8) = 109
    (1 * 3) + (2 * 5) + (4 * 6) + (8 * 9) = 109
    (1 * 3) + (2 * 7) + (4 * 5) + (8 * 9) = 109
    (1 * 4) + (2 * 6) + (3 * 7) + (8 * 9) = 109
    (1 * 4) + (2 * 8) + (5 * 7) + (6 * 9) = 109
    (1 * 5) + (2 * 6) + (4 * 9) + (7 * 8) = 109
    (1 * 5) + (2 * 7) + (3 * 6) + (8 * 9) = 109
    (1 * 6) + (2 * 5) + (3 * 7) + (8 * 9) = 109 <– Christians solution
    (1 * 6) + (3 * 9) + (4 * 5) + (7 * 8) = 109
    (1 * 7) + (2 * 3) + (4 * 6) + (8 * 9) = 109
    (1 * 7) + (2 * 4) + (5 * 8) + (6 * 9) = 109
    (1 * 8) + (2 * 4) + (5 * 6) + (7 * 9) = 109
    (1 * 8) + (3 * 4) + (5 * 7) + (6 * 9) = 109 <– Jmacs solution
    (1 * 8) + (3 * 6) + (4 * 5) + (7 * 9) = 109
    (2 * 6) + (3 * 7) + (4 * 9) + (5 * 8) = 109 <– Sofia Orefices, cellazac000s and Kaylas solution
    (2 * 6) + (3 * 8) + (4 * 7) + (5 * 9) = 109 <– Mistis solution
    (2 * 7) + (3 * 6) + (4 * 8) + (5 * 9) = 109 <– Olivia Wilkes, Martens and Daniels solution
    (2 * 7) + (3 * 9) + (4 * 5) + (6 * 8) = 109
    (2 * 8) + (3 * 5) + (4 * 9) + (6 * 7) = 109
    (2 * 9) + (3 * 5) + (4 * 7) + (6 * 8) = 109 <– javon montgomerys, Danitza Marencos, Lilys and Scarlett Salaz' solution

  25. (4 x 2) + (7 x 8) + (5 x 9) + (0 x 6) = 109

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