# Find the pattern in the months

$\text{April} \times \text{May} - \text{June} = \text{December} - \text{January}$

$\text{September} \div \text{November} \times \text{December} = \text{March} \times \text{March}$

$\text{January} \times \text{February} \div (\text{February} + x ) = \text{April}$

These three equations follow a certain pattern. What month of the year fits in the spot marked $x$? Please provide a logical explanation as well.

• Are the mathematical operators as one would expect? i.e. Is '*' ordinary multiplication and '/' division as we commonly think of it? Jun 13 '16 at 18:31
• Yes, they are exactly what you use in maths. :)
– user25136
Jun 13 '16 at 18:33
• @LUNA was this found in an IQ-test or did you make it up? Jun 13 '16 at 18:51
• Oh, I've come up with it myself. Looks like I put in the "iq-test" tag.
– user25136
Jun 13 '16 at 18:53

August

The math works as follows:

On the left side of the equation, the months represent the count of letters in their names (January = 7, February = 8, etc.).

On the right side of the equation, the months represent their location in the calendar (January = 1, February = 2, etc.).

To solve for the missing month, we have:

$7 \times 8 \div (8 + x) = 4$
$56 \div (8 + x) = 4$
$56 = 4(8 + x)$
$56 \div 4 = 8 + x$
$14 = 8 + x$
$14 - 8 = x$
$x = 6$

The only month with

$6$ letters in its name is August, so that is the solution.

• Ah, Ninja'd. Oh well.
– P...
Jun 13 '16 at 18:59

My guess:

August.

Reasoning:

The first two equations work if you replace months with the number of letters in their names on the left side of '=' and with their order in the year on the right side:

5 * 3 - 4 = 11 = 12 - 1
9 / 8 * 8 = 9 = 3 * 3
7 * 8 / (8 + _) = 4

6 is the number that fits in the gap, and August has six letters in its name.