Occasional Puzzles - ➕ Mix and Match
APRIL FOOLS!! Okay, okay, we couldn't resist. 😈
As you may have discovered, yesterday's puzzle was actually impossible. Scroll down to the solution for a full explanation.
And don't worry, we promise today's puzzle is solvable.
Today's Puzzle - ➕ Mix and Match
Move two matchsticks to create a new (and still correct!) equation. The following symbols are not allowed: ≠<>≤≥
Note: There are multiple correct solutions, so bonus points if you send in more than one!
Source: Reddit (warning: spoilers)
Source: The Kid Should See This
Previous Puzzle - 🔢 Breaking Even
Puzzle
Fill in the following 3x3 grid with the numbers 1-9 such that the sum of each row and the sum of each column is even. Each number can only be used once.
Solution [SPOILER]
There is no solution; the puzzle is impossible! Here's why:
Since the outcome we care about is whether the row and column sums are even, we don't even need to look at the numbers themselves. For the sum of three numbers to be even, they must either be all even, or be two odd numbers (which always sum to an even number) and one even number. So let's abstract away from the numbers and just look at odd vs. even.
In the numbers 1-9, there are five odd numbers and four even numbers. Let's start by trying to make one even column with three evens. That gives us something that looks like this:
| E | ||
| E | ||
| E |
Now we have one even number left to place, but nowhere for it to go! No matter where you put it, because there is exactly one remaining even number, there will inevitably be a row with two even numbers and one odd number, so you'll have at least one row that sums to an odd number. The same argument applies in any of the three columns, or if you made any of the three rows all evens. So putting three evens together is a no-go.
It's no use trying to put just two evens in one column, because we know that would create an odd column.
So the only other thing we can try is to put one even number in each column:
| E | ||
| E | ||
| E |
Well, this puts us in the same situation as the all-evens column. We again have one more even number to place, but nowhere to put it that doesn't create a row or column with only two even numbers (and thus an odd sum).
And so, the puzzle is impossible. We hope we didn't cause you too much grief!