Question P6 Repeated identity
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A candle maker packs a rectangular storage box tightly with 27 identical large cube-shaped candles and some identical small cube-shaped candles, so that candles of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of candles packed in the box.
Answer
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One length or count, described two ways in the same question.
In this one. The figure gives no lengths — but two blocks spanning the same depth fix the edge ratio 5 : 3, and that ratio alone counts every candle; the volume is only needed at the very end.
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
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