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Molawana: Dipalo tso 5 tse di tlhakanang go re palo e e fa gare mo naleding.

Mathematics

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here are the solutions for the puzzles:

a. Go batla dipalo (Find the numbers)

  • Rule: The numbers in each row must add up to 16.

    • Row 1: 2+5+3+6=162+5+3+6 = 16. (This row is complete.)
    • Row 2: We need three numbers that, when added to 2, sum to 16. So, the three numbers must sum to 16−2=1416-2=14. Let's use 4,5,54, 5, 5. 4+5+5+2=164+5+5+2 = 16
    • Row 3: We need three numbers that, when added to 2, sum to 16. So, the three numbers must sum to 16−2=1416-2=14. Let's use 3,6,53, 6, 5. 3+6+2+5=163+6+2+5 = 16

    The completed grid is:

    [253645523625]\begin{bmatrix} 2 & 5 & 3 & 6 \\ \boxed{4} & \boxed{5} & \boxed{5} & 2 \\ \boxed{3} & \boxed{6} & 2 & \boxed{5} \end{bmatrix}

b. Go batla dipalo (Find the numbers)

  • Rule: 3 numbers across rows and down columns add up to the same total.

    • Grid 1 (Left):

      • First, find the constant sum. Row 1: 2+7+6=152+7+6 = 15. Column 3: 6+1+8=156+1+8 = 15. The constant sum is 15.
      • Fill the missing numbers: Row 2: 9+5+1=15  ⟹  10+5=15  ⟹  59 + \boxed{5} + 1 = 15 \implies 10 + \boxed{5} = 15 \implies \boxed{5}. Row 3: 4+3+8=15  ⟹  4+11=15  ⟹  4\boxed{4} + 3 + 8 = 15 \implies \boxed{4} + 11 = 15 \implies \boxed{4}.
      • Check columns: Column 1: 2+9+4=152+9+4 = 15. Column 2: 7+5+3=157+5+3 = 15. Column 3: 6+1+8=156+1+8 = 15.

      The completed grid is:

      [276951438]\begin{bmatrix} 2 & 7 & 6 \\ 9 & \boxed{5} & 1 \\ \boxed{4} & 3 & 8 \end{bmatrix}
    • Grid 2 (Right):

      • First, find the constant sum. Row 1: 23+28+21=7223+28+21 = 72. The constant sum is 72.
      • Fill the missing numbers: Row 2: 12+34+26=72  ⟹  38+34=72  ⟹  3412 + \boxed{34} + 26 = 72 \implies 38 + \boxed{34} = 72 \implies \boxed{34}. Column 2: 28+34+10=7228 + 34 + 10 = 72. (This column is complete and correct.) Column 1: 23+12+37=72  ⟹  35+37=72  ⟹  3723 + 12 + \boxed{37} = 72 \implies 35 + \boxed{37} = 72 \implies \boxed{37}. Column 3: 21+26+25=72  ⟹  47+25=72  ⟹  2521 + 26 + \boxed{25} = 72 \implies 47 + \boxed{25} = 72 \implies \boxed{25}.
      • Check Row 3: 37+10+25=7237+10+25 = 72.

      The completed grid is:

      [232821123426371025]\begin{bmatrix} 23 & 28 & 21 \\ 12 & \boxed{34} & 26 \\ \boxed{37} & 10 & \boxed{25} \end{bmatrix}

c. Kwala dipalo dingwe fela tse 5 tse di tlhakanang go re palo e e fa gare mo naleding. (Write any 5 numbers that add up to the number in the middle of the star.)

  • Star 1 (Center 50): We need 5 numbers that sum to 50. Here is one possible solution:

    5+10+15+8+12=505+10+15+8+12 = 50

    The numbers are: 5,10,15,8,12\boxed{5}, \boxed{10}, \boxed{15}, \boxed{8}, \boxed{12}.

  • Star 2 (Center 120): We need 5 numbers that sum to 120. Here is one possible solution:

    10+20+30+25+35=12010+20+30+25+35 = 120

    The numbers are: 10,20,30,25,35\boxed{10}, \boxed{20}, \boxed{30}, \boxed{25}, \boxed{35}.

  • Star 3 (Center 150): We need 5 numbers that sum to 150. Here is one possible solution:

    20+30+40+25+35=15020+30+40+25+35 = 150

    The numbers are: 20,30,40,25,35\boxed{20}, \boxed{30}, \boxed{40}, \boxed{25}, \boxed{35}.

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