Privacy Policy

Terms & Conditions

See Details We use cookies to personalise content and ads. We also share information about your use of our site with our advertising partners who may combine it with other information you've provided to them or they've collected from your use of their services.
At the recent BrainBashers 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.
Alan was never last. Charles always beat Darren. Brian had at least one first place. Alan finished third in at least one of the races. Both Darren and Charles had a second place.
To explain  since Charles always beat Darren and Darren had a second place, one race must have been Charles first and Darren second. Brian therefore won the other race with Charles second. Since only one runner finished in the same place in both races, this must have been Alan in third. QED.
Puzzle 324
Practical Peter was asked to cut a 99 foot rope into three smaller, equal length ropes.
However, as usual, Pete couldn't find his measuring tape so he guessed!
When he finally did find his tape (it was under his hat), he discovered that:
A) the second piece of rope was twice as long as the first piece, minus 35 feet (i.e. 2 x first,  35).
B) the third piece of rope was half the length of the first, plus 15 feet (i.e. 0.5 x first, + 15)
Answer:
First = 34 feet.
Second = 33 feet.
Third = 32 feet.
This question can be solved easily using algebra, if we call the length of the first rope A, we have:
Rope 1 = A
Rope 2 = 2 x A  35
Rope 3 = 1 ÷ 2 x A + 15
The three ropes add to 99 feet, so:
99 = Rope 1 + Rope 2 + Rope 3
99 = A + (2 x A  35) + 1 ÷ 2 x A + 15
99 = 3.5 x A  20
Adding 20 to both sides we have:
119 = 3.5 x A
So:
A = 119 ÷ 3.5
A = Rope 1 = 34 feet
Rope 2 = 2 x 34  35 = 68  35 = 33 feet
Rope 3 = 1 ÷ 2 x A + 15 = 1 ÷ 2 x 34 + 15 = 17 + 15 = 32 feet
Just to check:
Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99.
As required. QED.
BrainBashers™ is a trademark. We use cookies to personalise content and ads. We also share information about your use of our site with our advertising partners who may combine it with other information you've provided to them or they've collected from your use of their services. For more information please view our privacy policy. By using the site you also agree to our terms and conditions.