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Complete the grid by counting in 2s with odd numbers and finding the column pattern. Numbers are added in columns by 16. This is a grid of 5x5.

Mathematics

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Step-by-step solution

6 steps

Here's the completed grid by counting in 2s with odd numbers.

  1. Complete Row 1.

    The given numbers are 1, 3, 5, and 9. To count in 2s with odd numbers, we add 2 to the previous number.
    5+2=75 + 2 = 7.
    Row 1: 1, 3, 5, 7, 9

  2. Complete Row 2.

    The given numbers are 17 and 19.
    19+2=2119 + 2 = 21
    21+2=2321 + 2 = 23
    23+2=2523 + 2 = 25
    Row 2: 17, 19, 21, 23, 25

  3. Complete Row 3.

    The given numbers are 33, 35, 37, and 39.
    39+2=4139 + 2 = 41
    Row 3: 33, 35, 37, 39, 41

  4. Determine the pattern for the columns.

    Let's look at the first column: 1, 17, 33.
    The difference between consecutive numbers is 17−1=1617 - 1 = 16 and 33−17=1633 - 17 = 16.
    This means each number in a column is 16 greater than the number above it.

  5. Complete Row 4.

    Using the column pattern, the first number in Row 4 is 33+16=4933 + 16 = 49.
    Then, fill the rest of the row by adding 2:
    49+2=5149 + 2 = 51
    51+2=5351 + 2 = 53
    53+2=5553 + 2 = 55
    55+2=5755 + 2 = 57
    Row 4: 49, 51, 53, 55, 57

  6. Complete Row 5.

    Using the column pattern, the first number in Row 5 is 49+16=6549 + 16 = 65.
    Then, fill the rest of the row by adding 2:
    65+2=6765 + 2 = 67
    67+2=6967 + 2 = 69
    69+2=7169 + 2 = 71
    71+2=7371 + 2 = 73
    Row 5: 65, 67, 69, 71, 73

    Here is the completed grid:

    135791719212325333537394149515355576567697173\boxed{ \begin{array}{|c|c|c|c|c|} \hline 1 & 3 & 5 & \textbf{7} & 9 \\ \hline 17 & 19 & \textbf{21} & \textbf{23} & \textbf{25} \\ \hline 33 & 35 & 37 & 39 & \textbf{41} \\ \hline \textbf{49} & \textbf{51} & \textbf{53} & \textbf{55} & \textbf{57} \\ \hline \textbf{65} & \textbf{67} & \textbf{69} & \textbf{71} & \textbf{73} \\ \hline \end{array} }
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