# Strange Hens and a half [closed]

If a hen and a half lays an egg and a half in day and a half, how many eggs will six hens lay in nine days?

• Half a hen can't lay an egg- dead hen. Half an egg would an awful mess. – user2617804 Oct 22 '17 at 9:18
• “If one and a half chickens lay one and a half eggs in one and a half days, how many eggs will nine chickens lay in nine days?” - Isaac Asimov, Escape, I, Robot. Look familiar? – Wen1now Oct 22 '17 at 10:28

Assuming there's no "gotchas!" with things like how half an egg could be laid etc. the answer is:

36 eggs

Reasoning:

If 1.5 hens lay 1.5 eggs in 1.5 days, then 1 hen will lay 1 egg in 1.5 days. 9 days is 6x1.5 day periods, so the 6 hens will each lay 6 eggs, for a total of 36 eggs.

x hens lay y eggs in z days.

x hens lay $y\times\dfrac{9}{z}$ eggs in 9 days.

6 hens lay $\dfrac{6}{x}\times y\times\dfrac{9}{z}$ eggs in 9 days.

In this case $x=y=z=\dfrac32$, so:

$$6\cdot\frac23\times\frac32\times9\cdot\frac23=4\times\frac32\times6=36\,\text{eggs}$$

• I eggspected for eggsample the half a hen would be eggspired then it shell lay duck eggs. – Tom Oct 22 '17 at 8:37
• $\pi$ hens lay $e$ eggs in $\phi$ days... – JMP Oct 22 '17 at 8:59

They will lay:

36 eggs

Because:

Hens   Eggs   Time
1.5    1.5    1.5
6      6      1.5
6      36     9