Published
Nine tiles, three kinds of weather, and three row totals. You can grind this one out the long way, but there’s a shortcut hiding in plain sight that gets you there in about ten seconds.
The puzzle
- Every sun is worth the same whole number. So is every leaf, and so is every raindrop.
- Top row: sun + sun + leaf = 17
- Middle row: leaf + leaf + raindrop = 11
- Bottom row: raindrop + sun + raindrop = 17
What does the left column (sun, leaf, raindrop) add up to? Bonus: what is each shape worth?
Show hint
You don’t need to know any single shape’s value to answer the main question. Count how many times each shape appears in the whole grid.
Show answer
Answer: the left column adds up to 15. (Sun = 7, leaf = 3, raindrop = 5.)
The shortcut:
- Count the shapes in the whole grid: there are exactly 3 suns, 3 leaves and 3 raindrops.
- So adding all three rows adds up three of each shape: 17 + 11 + 17 = 45 = 3 × (sun + leaf + raindrop).
- That means one of each shape is worth 45 ÷ 3 = 15, and the left column is exactly one sun, one leaf and one raindrop.
The bonus, the long way:
- The top row says 2 suns + 1 leaf = 17, so a leaf is 17 − 2 × sun.
- The middle row says 2 leaves + 1 raindrop = 11, so a raindrop is 11 − 2 × leaf.
- Try sun = 7: leaf = 17 − 14 = 3, raindrop = 11 − 6 = 5. Check the bottom row: 5 + 7 + 5 = 17. ✓ (Substituting all the way through gives 9 × sun = 63, so 7 is the only answer.)
And the shortcut agrees: 7 + 3 + 5 = 15. When every symbol shows up the same number of times, adding everything at once often beats solving for each piece.