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Sagot :
Solution
- Let the numbers be:
a1 + a2 ÷ a3 = 2
x + +
a4 - a5 + a6 = 5
- + +
a7 + a8 + a9 = 13
= = =
15 15 15
- Now let us write ou the possible equations:
[tex]\begin{gathered} a_1+a_2\div a_3=2 \\ a_1+\frac{a_2}{a_3}=2\text{ \lparen Equation 1\rparen} \\ \\ a_4-a_5+a_6=5\text{ \lparen Equation 2\rparen} \\ \\ a_7+a_8+a_9=13\text{ \lparen Equation 3\rparen} \\ \\ a_1\times a_4-a_7=15 \\ a_1a_4-a_7=15\text{ \lparen Equation 4\rparen} \\ \\ a_2+a_5+a_8=15\text{ \lparen Equation 5\rparen} \\ \\ a_3+a_6+a_9=15\text{ \lparen Equation 6\rparen} \end{gathered}[/tex]- I do not think this will get us anywhere very quickly.
- Guessing the numbers, we have that:
The ways to get the first horizontal equation are:
The first horizontal equation equates to 2. This means that the equation is essentially 1 + 1 since there are no negative operations. So we have:
1 + 2 / 2 = 2
1 + 7 / 7 = 2
The second horizontal equation equates to 5. There is an addition and a subtraction. Only two sets of positive integers add up to 5. 2 + 3 or 1 + 4. Some other equations exist: -2 + 7 and -4 + 9 and -3 + 8 and -1 + 6
This makes the possibilities for this second horizontal equation greater.
The third horizotal equation equates to 13. All additions. this means that we can have:
6 + 7 = 2 + 4 + 7
5 + 8 = 1 + 4 + 8
4 + 9 = 2 + 2 + 9 = ...
The first vertical equation equates to 15.
The first two numbers multiply and the result is subtracted from a number to get 15.
- We must subtract an odd number from an even number to get an odd number(15).
- Thus, the possibilities of the result of the product are:
(15 + 7), (15 + 1), (15 + 9) = 22, 16, 24
- 22 is out of it since none of the numbers given multiply to give 22.
- 16 = 2 x 8
24 = 6 x 4
- The first horizontal row establishes that the first number must be a 1. However, there is no way to fit a 1 in the first cell in the vertical column. as we just showed.
- Because of these, I do not think the values given work.
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