How a Double-Layer Window System Reduces Solar Heat to One-Third

In a Guardian science puzzle published on 20 July 2026, readers are asked to determine what fraction of incoming solar energy reaches a room when both roller blinds and curtains cover a window. The scenario assumes homogeneous materials, equilibrium heat flow, and ignores glass, colour, and room geometry. The blinds lie directly against the window; the curtains hang over the blinds. Each layer, when heated, radiates half of the absorbed energy back toward the window and half forward into the room.

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When equilibrium is reached, the curtain absorbs energy = 2 h (where h is the amount it radiates forward). Consequently, the blind must supply those 2 h plus the energy it receives back from the curtain (h), meaning the blind radiates 4 h total. Of that 4 h, only 3 h originates from the Sun; the remaining h is re-radiated solar energy reflected by the curtain. Since the curtain passes only h into the room, the room receives h out of the original 3 h solar input, i.e., 33 percent of the Sun’s energy. The puzzle deliberately challenges the intuitive 25 percent answer (½ × ½) by emphasizing the cumulative heat-exchange dynamics at equilibrium.

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The column, authored by an unnamed Guardian writer and credited to puzzle creator Alan Williams-Key, has run on alternate Mondays since 2015. It blends informal problem-posing with brief physical reasoning, inviting readers to “think like a physicist” rather than apply formal equations. The piece is presented as a recreational challenge rather than a peer-reviewed scientific analysis.

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• “In other words, curtains stop 50 per cent of the energy from the Sun.” — Alan Williams-Key, puzzle creator

The Guardian

• “Think like a physicist.” — Alan Williams-Key, puzzle creator

The Guardian

• “NO SPOILERS PLEASE.” — Alan Williams-Key, puzzle creator

The Guardian

• “I hope you enjoyed this puzzle.” — Alan Williams-Key, puzzle creator

The Guardian