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Puzzle 517
Practical Pat was asked to cut a 99 foot rope into three smaller, equal length ropes.
However, as usual, Pat couldn't find the measuring tape, so a guess took place!
When the tape was finally found (it was under a hat), Pat discovered that:
the second piece of rope was twice as long as the first piece, minus 35 feet the third piece of rope was half the length of the first, plus 15 feet
How long were each of the pieces of rope?
Answer
First = 34 feet.
Second = 33 feet.
Third = 32 feet.
Reasoning
This question can be solved 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 = 0.5 x A + 15
The three ropes add to 99 feet: 99 = Rope 1 + Rope 2 + Rope 3 99 = A + (2 x A – 35) + (0.5 x A + 15) 99 = 3.5 x A – 20 119 = 3.5 x A 34 = A
For being well-behaved at the garden fayre, four children were each given two sweets.
Jesse had an orange sweet. One child who had a red sweet also had a blue one. No child had two sweets of the same colour. A child who had a green sweet also had a red one. Jamie didn't have a red sweet, and Jo had a green one. Jordan didn't have an orange one, and Jesse had no blue sweets.
Knowing that there were two sweets of each colour, can you tell the colours of the sweets each child had?
Answer
Jamie Orange Blue
Jesse Orange Green
Jo Green Red
Jordan Red Blue
Reasoning
The children were: Jamie, Jesse, Jo, Jordan.
The colours were: Blue, Green, Orange, Red.
There were two sweets of each colour, and by (3) no child had two sweets of the same colour.
By (1), Jesse had an Orange sweet …
… by (6), didn't have Blue …
… by (2) and (4), Red was paired with Blue and Green …
… therefore, Jesse's other sweet can't have been Red, so was Green.
Jamie
Jesse Orange Green
Jo
Jordan
By (4) the other Green sweet was paired with Red, by (5) this must have been Jo.
Jamie
Jesse Orange Green
Jo Green Red
Jordan
By (2) the other Red sweet was paired with Blue, but by (5) this wasn't Jamie, so must have been Jordan.
Jamie
Jesse Orange Green
Jo Green Red
Jordan Red Blue
Leaving Jamie with Orange and Blue.
Jamie Orange Blue
Jesse Orange Green
Jo Green Red
Jordan Red Blue
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Puzzle 519
How many squares of any size on this chessboard do not contain a rook?
Answer
Here are the contents of the containers after each stage:
A = 9 litres, B = 4 litres
A B
9 0 fill A
5 4 fill B from A (leaving 5 litres in A)
5 0 empty B
1 4 fill B from A (leaving 1 litre in A)
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A (only 3 more litres fit in B)
6 0 empty B
This leaves 6 litres in container A.
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
