Function Puzzle — Local Means Edition

Timer: 90s Goal: Place the five pieces in the correct order.

Segment Means (given):

Hints:
  • The function is defined on [0,10] and cut into five pieces of equal width.
  • The horizontal line in each tile is the x-axis (y = 0).
  • Use continuity of the curve and the average value of each segment to decide the order.

What is BMO?

BMO stands for Bounded Mean Oscillation. A function is in BMO if, on every interval, its average deviation from the interval’s mean is uniformly bounded. Intuitively, a BMO function may wiggle, but it does not wiggle “too much” on average over any local window. This puzzle echoes that idea: by looking at the local means of pieces, you infer the global structure of the function.