Can eight sums march in step?
Give six cube faces different integers. Make the eight corner sums form an evenly spaced sequence.
The clock starts when you reveal the puzzle.SIX FACES. EIGHT CONNECTED POSSIBILITIES.
Number the faces.
Find the rhythm.
Three faces meet.
Eight sums fall into place.
A CUBE, UNFOLDED
Opposite faces: Left ↔ Right · Top ↔ Bottom · Front ↔ Back
EIGHT CORNER SUMS · SMALLEST FIRST
Tap a sum to inspect its three facesEnter six different integers. At each corner, add the three faces that meet there.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
Eight sums.
Three choices behind them.
Explore your own face numbers, then uncover the structure of the gaps.
YOUR EIGHT CORNERS
CHOOSE ONE FROM EACH OPPOSITE PAIR
One cube. Three independent switches.
A corner uses one of Left or Right, one of Top or Bottom, and one of Front or Back. That makes 2 × 2 × 2 = eight combinations.
Begin with the smaller number from each pair. Switching to the larger face adds that pair’s difference. To get every step exactly once, use differences in the ratio 1 : 2 : 4.
Those switches create 0, 1, 2, 3, 4, 5, 6 and 7 steps above the smallest sum. Each choice has its own three-bit pattern: the same place-value idea used in binary numbers.
Why are those differences forced? The first step needs a switch of size one step. The next uncovered value is two steps, so another switch must provide two. The first two switches cover through three; the last must provide four. Scale all three differences together to change the gap.
The idea to take away
Look for independent choices hiding inside a connected picture. Three two-way choices can generate eight carefully structured results.