Can 1,2,3,4,5,6,7 equal 2010 with only three equations?
To determine if the numbers 1, 2, 3, 4, 5, 6, and 7 can be used in three equations to equal 2010, we can approach this problem mathematically.
Let's assume we can use addition, subtraction, multiplication, and division to form the equations. Here's how we can proceed:
1. First, let's consider the sum of all the numbers:
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
However, the sum of these numbers is far less than 2010, so it is not possible to reach 2010 using addition alone with these numbers.
2. Next, let's try multiplying the numbers together:
1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040
But again, the product is significantly larger than 2010.
3. Since addition and multiplication alone won't work, we can try different combinations of addition, subtraction, multiplication, and division.
For example, let's consider the following equations:
7 x 6 x 5 x 4 - 3 x 2 - 1 = 840 - 6 - 1 = 833
We can see that this equation is much smaller than 2010.
However, by trying out different combinations of operations and numbers, it becomes clear that it is impossible to reach 2010 using only three equations with these specific numbers (1, 2, 3, 4, 5, 6, and 7).
Hence, it is not possible to equal 2010 using only three equations with the given numbers.