Brain Teasers · The Broken Clock
Broken Clock Puzzle - Three Pieces That Sum to 26
A clock breaks into three pieces along two straight cracks, and each piece's numbers add up to the same total.
What is the broken clock puzzle?
It is an invariant puzzle: the total of 1 to 12 is fixed at 78, so three equal pieces must each total 26.
The shape of the pieces does the rest. Two straight cracks that don't cross give two end pieces of neighbouring numbers and a middle strip.
How it works
A wall clock falls and breaks into three pieces along two straight cracks. No number is split, and the three totals match. The story asks which numbers are on each piece. You pick one of four answers. Then you step through the answer and the breakdown.
How scoring works
This teaser checks your answer. A wrong pick is crossed out. You get two tries before the answer opens. A correct first try earns a ticket; a second try or opening the answer early is recorded but earns nothing. The story teasers share one lifetime unlock for free users.
The key insight
Each piece sums to 78 / 3 = 26. The only runs of neighbouring numbers that sum to 26 are 11-12-1-2 and 5-6-7-8, and what's left, 3-4-9-10, also sums to 26 and forms the strip between two parallel cracks.
The full step-by-step solution lives at /brain-teasers/broken-clock/solution.
A worked example
One crack runs from between 10 and 11 to between 2 and 3, the other from between 8 and 9 to between 4 and 5.
Common mistakes
• Looking for three pie slices of four numbers each.
• Starting with guesses instead of the total of 78.
• Allowing the cracks to cross, which gives four pieces.
Why interviews test this
This tests starting from what can't change, then using the geometry to cut the search down. The written solution is at /brain-teasers/broken-clock/solution.
Play The Broken Clock on Outcry
The Broken Clock is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play The Broken Clock and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.