Question

Place the numbers 1 to 9 to make valid equation.
_+ 13 × _ ÷ _ + _ + 12 × _ - _ - 11 + _ × _ ÷ _ - 10 = 66

Answer 1

Thanks for this interesting Maths puzzle.

It is very easy to solve.

The question is to place the numbers 1 to 9 in such a way that each number is used once to make a valid equation.


_+ 13 × _ ÷ _ + _ + 12 × _ - _ - 11 + _ × _ ÷ _ - 10 = 66


The next step is to select the order of operations. Multiplication and division take precedence over addition and subtraction according to BODMAS rule.

So we add parentheses to evaluate them first.

_ + (13 x _ / _) + _ + (12 x _) – _ – 11 + (_ x _ / _) – 10 = 66

There are several solutions:----

1. 9 + (13 x 4 / 8) + 5 + (12 x 6) – 7 – 11 + (1 x 3 / 2) – 10 = 66

2. 9 + (13 x 4 / 8) + 5 + (12 x 6) – 7 – 11 + (3 x 1 / 2) – 10 = 66

3. 5 + (13 x 4 / 1) + 9 + (12 x 2) – 7 – 11 + (3 x 8 / 6) – 10 = 66

4. 5 + (13 x 9 / 3) + 6 + (12 x 2) – 1 – 11 + (7 x 8 / 4) – 10 = 66

5. 6 + (13 x 3 / 1) + 9 + (12 x 2) – 5 – 11 + (7 x 8 / 4) – 10 = 66

Hope it helps!