A hen and a half lays an egg and a half

Question

If a hen and a half lays an egg and a half in a day and a half, how many eggs do six hens lay in six days? The knee-jerk answer is six. Check it by first working out what a single hen produces in a single day, and then explain exactly where the knee-jerk reasoning goes wrong.

Accepted Answer

Twenty-four eggs. One hen, one day. A hen and a half lays an egg and a half in a day and a half. So one hen lays one egg in a day and a half (divide the hens and the eggs by 1.5, keeping the time). Therefore one hen lays 2/3 of an egg per day. Scale up. Six hens lay 6 × 2/3 = 4 eggs per day. In six days: 4 × 6 = 24 eggs. Why six is wrong. The tempting reasoning is "1.5 hens, 1.5 eggs, 1.5 days, so 6 hens, 6 eggs, 6 days", scaling all three numbers by four. But eggs scale with hens and with days, so multiplying both hens and days by 4 multiplies the eggs by 16: 1.5 × 16 = 24. The general rule.…

A hen and a half lays an egg and a half

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