Can six different areas fit?
Cover a 7 × 7 board with six rectangles. Every area must be different, and every side at least 2 cells long.
The clock starts when you reveal the puzzle.THE AREAS HAVE TO FIT TOO
Six rectangles.
Every area different.
Forty-nine cells.
No narrow shortcuts.
Tap opposite corner cells, or drag. Arrow keys + Enter work too.AT YOUR OWN PACE
A brain snack, with room to think.
THE ANSWER OPENS ANOTHER DOOR
Now for the lovely part.
You have an answer. Explore how it works, then take the idea somewhere new.
See why it works ↓Keep your time
THE IDEA BEHIND YOUR ANSWER
The areas were forced.
The arrangement was yours.
Explore your six rectangles, then see how counting narrows the problem before the first piece is drawn.
LET AREA DO THE FIRST PART
Six smallest areas. Exactly enough space.
With both sides at least 2, the smallest possible rectangle has area 4. The next different possible areas are 6, 8, 9, 10 and 12. Areas 5, 7 and 11 cannot be made by multiplying two whole numbers that are both at least 2.
4 + 6 + 8 + 9 + 10 + 12 = 49
These are already the six smallest different areas, and they use the whole board. Replacing any with a larger area would exceed 49. So every solution must use this exact set.
| Area | Your rectangle |
|---|
AREA IS NECESSARY. FIT IS ANOTHER QUESTION.
Twelve has a choice.
The board does not.
The idea to take away
Count first, then arrange. A numerical constraint can force the pieces, while geometry decides how those pieces can fit.