A thief gets a head start, but his steps are shorter than the officer's
A constable spots a thief exactly 27 of the constable's own steps ahead and sets off in pursuit at once. While the constable takes 5 steps, the thief manages 8, but the thief's steps are shorter: every 2 steps the constable takes cover the same ground as every 5 steps the thief takes. How many steps does the constable need to take before he catches the thief?
Reveal the answer
30 steps. In the time it takes the constable to cover that ground, the thief covers 48 of his own steps, which, added to his 27-step head start, comes to a distance exactly equal to 30 of the constable's longer steps. Henry Dudeney published this as 'Catching the Thief' in Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — Thomas Nelson & Sons, 1917
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