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Answer: 1806
Square numbers near 1871 (year of death)
40$\times$40 = 1600 too small
42$\times$42 = 1764, but if he was 42 in 1764 then by 1871 he was older than 140
43$\times$43 = 1849, 22 years before he died in 1871, which is reasonable
44$\times$44$\gt$1871 so there are no more possibilities
So he was born 43 years before 1849, in 1806
Age of Augustus
Age 11 to 14
ShortChallenge Level 
Answer: 1806
Square numbers near 1871 (year of death)
40$\times$40 = 1600 too small
42$\times$42 = 1764, but if he was 42 in 1764 then by 1871 he was older than 140
43$\times$43 = 1849, 22 years before he died in 1871, which is reasonable
44$\times$44$\gt$1871 so there are no more possibilities
So he was born 43 years before 1849, in 1806
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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