Answers to last issue's Brain Teasers
1. Yesterday I went for a long bicycle ride around the local lakes. As the ride was quite long, I rode in various stages. In the first stage I rode half of the overall distance. Stage two saw half of the remaining distance plus 35 metres covered. Stage three covered three-quarters of the remaining distance. Stage four completed half of the remaining distance plus 75 metres. Stage five completed the journey with a final burst of 150 metres. How far did I cycle in total?
Ans: 7,340 metres. How do we get this? It's simplest to work forwards and then back again. Let the total distance be X. Then I cycled half the distance, X/2, in the first stage. So X/2 distance was left. I cycled half of this plus 35 m in the second stage, so that is (1/2)(X/2)+35 or X/4+35 m. So the amount left was X/4-35 m.  In stage 3, I cycled 3/4 of this distance, (3/4)(X/4-35), so (1/4) was left over: (1/4)(X/4-35). In stage 4, I cycled (1/2) this remaining distance plus 75 m, that is (1/2)(1/4)(X/4-35)+75=(1/8)(X/4-35)+75, so the other half minus 75 m was left over: (1/8)(X/4-35)-75, and I cycled it all in the fifth stage. Also, this amount of journey was 150 m.
So (1/8)(X/4-35)-75=150 m, or (1/8)(X/4-35)=(150+75)=225 m, or (X/4-35)=8X225=1800 m, or (X/4)=1835 m or X=1835X4=7340 m.
Counting backwards, in stage 1, I cycled 3,670 m, leaving 3,670 m, in stage 2, I cycled 1,870 m, leaving 1,800 m, in stage 3, I cycled 1,350 m, leaving 450 m, in stage 4, I cycled 300 m, leaving 150 m, and in stage 5, I cycled 150 m, leaving 0 m.

2. At the recent Sports Festival, the 100 metres heats were closely monitored. Each contestant had to run in two races so that the average place could be determined. Only one runner finished in the same place in both races. Abhay was never last. Charlie always beat Dilkush. Bharati had at least one first place. Abhay finished third in at least one of the races. Both Dilkush and Charlie had a second place. What were the results of the two races?
Ans: This is a logic puzzle. Let's start with the fact that Charlie always beat Dilkush. But Dilkush has a second place in one race. Let's call it Race 1. So Charlie had to be first in that race. Then Bharati was first in the other race, Race 2. And since both Charlie and Dilkush had a second place each, Charlie must have been second in Race 2. So now we have to find third and fourth place in each race. But Abhay was never last, and so he was third in both (and was the only runner to finish in the same place in both races). So Bharati came last in Race 1 and Dilkush came last in Race 2. So the results are
Race 1: Charlie, Dilkush, Abhay, Bharati.
Race 2: Bharati, Charlie, Abhay, Dilkush.
From http://www.brainbashers.com/