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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 202

If a hen and a half lay an egg and a half in a day and a half, how many eggs can a hen lay in three days?

[Ref: ZRKN]

Hint: Try doubling the number of hens first.

Answer: 2 eggs.

We are told that:

1.5 hens will lay 1.5 eggs in 1.5 days.

We can double the chickens (which doubles the eggs):

3 hens will lay 3 eggs in 1.5 days.

We can now double the days (which doubles the eggs):

3 hens will lay 6 eggs in 3 days.

We can now divide the number of hens by 3 (which also divides the numbers of eggs by 3).

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.

Puzzle 205

Using the BrainTracker grid below, how many words can you find? Each word must contain the central P and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?

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