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Weekly puzzle solution: A friendly bicycle race


Welcome to GeniiOnline’s Weekly Puzzle, powered by Art of Play! We’ll bring you a new puzzle every Monday, then publish the solution on Tuesday.

In case you missed the puzzle yesterday, here it is again: 

At the Buck family reunion, five sets of twins from five different generations decide to have a bike race, with two teams and one sibling from each set of twins on each team. Each team sets off with all five cyclists in a line behind their “captain”. At any point in the race, the last person in the line can cycle to the front of the line to become the new captain. All five team members must cross the finish line to complete the race.

Both teams line up in age order but Team A starts the race with a little kid as their captain and Team B starts the race with an elderly woman as their captain. During the course of the race, the captains change six times between the two teams. When the teams cross the finish line, what are the odds that their captains will be the same age?

ANSWER:

100 per cent. Lets call the five sets of twins in age ascending order 1A and 1B, 2A and 2B, 3A and 3B, 4A and 4B and 5A and 5B.

So, Team A starts in this order 1A 2A 3A 4A 5A

Team B starts 5B 4B 3B 2B 1B

The last person replaces the first person six times. So either one team does it six times and the other zero, or five times and one time, or four and two, or three and three. You will see that in each case, the leaders of the teams are the same set of twins.

For example, let’s say Team A replaces its leader once. The order will then be 5A 1A 2A 3A 4A. And let’s say Team B replaces its leader five times. Which puts them back to the starting formation 5B 4B 3B 2B 1B. Twins 5A and 5B – who have the same age! – are the finishing captains for their teams.

Come back next Monday for a new puzzle! And if you missed last week’s brainteaser, check it out here.