Open Middle®
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.
Answer 2: (4 x 8) + (7 x 2) + (3 x 6) + (9 x 5 )= 109
** There are probably more correct answers.
Source: Linda Hutcheson
9×8=72
7×3=21
5×2=10
1×6=6
72+21+10+6=109 😀
(4×3)+(7×2)+(3×6)+(9×2)=109
(6×8)+(7×4)+(3×5)+(9×2)=109
(6×8)+(7×4)+(3×5)+(9×2)=109 is what i got
9×5+3×8+4×7+2×6=109
5×5, 5×5, 4×7, 4×7,
Each number used only once, at most.
(7X5)+(6X6)+(8X3)+(2X7)=109
THIS IS MY ANSWER
4×9 5×8 7×3 6×2 is 109.
6X8=48 9X2=18 7X4=28 3X5=15 total is 109
48+18+28+15=109
5×8 + 7×3 + 4×9 x 6×2=109
(7×5)(6×6)(8×3)(2×7)=109
6X8=48 9X2=18 7X4=28 3X5=15 total is 109
48+18+28+15=109
（5*9）+（3*8）+（3*5) + (5*5)=109
45+24+15+25=109
(6 x 8= 52)
(7 x 5= 35)
(5 x 2= 10)
(4 x 3= 12)
52+35+10+12=109
(4 x 8) + (7 x 2) + (3 x 6) + (9 x 5 )= 109
Answer 1: ( 6 x 8)+ (7 x 4) + (3 x 5) + (9 x 2) = 109
Answer 1: ( 6 x 8)+ (7 x 4) + (3 x 5) + (9 x 2) = 109 is this it
(6 x 8)+ (7 x 8)+ (3+5)+ (9 x 2) = 109
(9 x 7) + (8 x 5) + (6 x 1) + (0 x 2) = 109
7×2=14
3×6=18
4×8=32
9×5=45
90+10=100+9=109
(9×8)+(7+5)+(2×1)+(0x6)=109
(4×8)+(7×2)+(3×6)+(9×5)=109
(6×9) + (5×7) + (3×4) + (1×8)
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
(4 x 2) + (7 x 8) + (5 x 9) + (0 x 6) = 109
9×3=27,7×8=56,2×1=2,6×4=24.27+56+2+24=109 this is our answer
We loved this challenge