Henry Ernest Dudeney/Puzzles and Curious Problems/73 - The Tube Stairs

by : $73$

 * The Tube Stairs
 * We ran up against Percy Longman, a young athlete, the other day when leaving Curley Street tube station.
 * He stopped at the lift, saying, "I always go up by the stairs.
 * A bit of exercise, you know.
 * But this is the longest stairway on the line -- nearly $1000$ steps.
 * I will tell you a queer thing about it that only applies to one other smaller stairway on the line.
 * If I go up two steps at a time, there is one step left for the last bound;
 * if I go up three at a time, there are two steps left;
 * if I go up four at a time, there are three steps left;
 * five at a time, four are left;
 * six at a time, five are left;
 * and if I went up seven at a time there would be six risers left over for the last bound.
 * Now, why is that?"


 * As he went flying up the stairs, three steps at a time, we laughed and said,
 * He little suspects that if he went up twenty steps at a time there would be nineteen risers for his last bound!"


 * How many risers are there in the Curley Street tube stairway?
 * The platform does not count as a riser, and the top landing does.