Question

John is playing a game in which he tries to obtain the highest number possible. He must put the symbols +, *, and - (plus, times, and minus) in the following blanks, using each symbol exactly once:

2_4_6_8
John cannot use parentheses or rearrange the numbers. What is the highest possible number that John could obtain?

Answer 1

2 - 4 + 6 x 8 = 46

Explanation:

We know that John can use each operation only once. Therefore, addition could be the first, second, or third operation from left to right. Likewise, subtraction could be the first, second, or third operation, and multiplication could be the first, second, or third operation. Recall that the multiplication must be the first operation to be performed because of the order of operations. Thus, the possible combinations are

2 + 4 - 6 x 8 = -42,

2 + 4 x 6 - 8 = 18,

2 - 4 + 6 x 8 = 46,

2 - 4 x 6 + 8 = -14,

2 x 4 + 6 - 8 = 6,

2 x 4 - 6 + 8 = 10.

Now, we can see that the highest possible number that John can obtain is 2 - 4 + 6 x 8 = 46.

Answer 2

• 2 - 4 + 6*8 = 46

Explanation:

There are 6 possible options:

• 2 - 4 + 6*8 = 46
• 2 - 4*6 + 8 = - 14
• 2 + 4 - 6*8 = - 42
• 2 + 4*6 - 8 = 18
• 2*4 - 6 + 8 = 10
• 2*4 + 6 - 8 = 6

As we the highest possible number is 46