This can be a tough sketch of the end of a race up a staircase through which three males took half. Ackworth, who’s main, went up three steps at a time, as organized; Barnden, the second man, went 4 steps at a time, and Croft, who’s final, went 5 at a time. Undoubtedly Ackworth wins. However the level is, what number of steps are there on the steps, counting the highest touchdown as a step? The highest of the steps are solely proven. There could also be scores, or tons of, of steps under the road. However it’s doable to inform from the proof the fewest doable steps in that staircase. Are you able to do it?
Given: Ackworth is in need of reaching the highest by just one step.
Puzzle – The Staircase Race
Resolution: If the staircase had been such that every man would attain the highest in a sure variety of full leaps, with out taking a decreased quantity at his final leap, then the smallest doable variety of steps would, after all, be 60 (that’s, 3 X 4 X 5). However it’s given to us that,
- Ackworth whereas taking three steps at a leap, has one odd step on the finish,
- Barnden taking 4 at a leap could have three solely on the finish and,
- Croft, taking 5 at a leap, could have 4 solely on the end.
Due to this fact, we have now to search out the smallest quantity that, when divided by 3, leaves a the rest of 1, when divided by 4 leaves 3, and when divided by 5 leaves a the rest of 4. This quantity is 19. So there have been 19 steps in all.
