Puzzles
The hundred-step dove ladder
A ladder has 100 steps. One dove perches on the first step, two doves on the second, three on the third, one more bird on each successive step all the way up, until the hundredth step holds a hundred doves. How many doves are perched on the ladder altogether?
Reveal the answer
5,050 doves. Alcuin's solution pairs the steps (1st+99th, 2nd+98th, and so on), each pair totaling 100 doves, giving 49 such pairs plus the 50th and 100th steps left over. It's "propositio de scala habente gradus centum" in the 9th-century manuscript Propositiones ad Acuendos Juvenes, attributed to Alcuin of York, a summation puzzle predating the schoolboy Gauss legend by roughly a thousand years.