A number leaves remainder 3 when divided by 5, remainder 4 when divided by 7 and remainder 5 when divided by 9. What is the smallest such number?

Numbers ≡ 5 (mod 9) and ≡ 4 (mod 7): 5, 14, 23, 32, 41, … — 32 is the first that leaves 4 on division by 7, so the numbers are 32 + 63k: 32, 95, 158, … Of these, 158 is the first leaving remainder 3 on division by 5.