House in Half

by Serhiy Grabarchuk Jr

Solution Step 0/0

Eight matchsticks are arranged into the pentagon resembling a house. Employing three additional matchsticks, divide the shape into two parts of the same area. Note: none of the three matchsticks must touch the matchstick A, even at its ends.

Of the five shape’s corners how many of them the dividing matchsticks will touch with their ends?


The shape’s area equals two full 1×1 squares and four 1x1x1 triangles. The half of it is 1 square and 2 triangles respectively. The diagram shows the solution where no matchstick touches either matchstick A or any of the shape’s corners, dividing the shape into two parts of the same area.

Check 1 corner
Check 2 corners
Check 3 corners
Check No touches at all