Puzzle 149
If a bottle weighs eight ounces plus half a bottle …
… what is the weight of a bottle and a half?
Puzzle Copyright © Kevin Stone
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Hint
Find the weight of the bottle first.
Answer
24 ounces.
The bottle weighs 16 ounces.
Reasoning
As a bottle (B) weighs eight ounces plus half a bottle, we can write this as:
B = 8 + 1/2 x B
1/2 x B = 8
B = 16
As the bottle weighs 16 ounces, a bottle and a half weighs 16 + 8 = 24 ounces.
Puzzle 150
Can you find three consecutive odd numbers that …
… total 7,644,585 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
195 x 197 x 199.
Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.
Let's try dividing by the closest odd number to 196.99:
7644585 ÷ 197 = 38805
We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.
Trying either 195 or 199 gives the answer.
Double-Checking
195 x 197 x 199 = 7,644,585
Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Puzzle 151
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?
Puzzle Copyright © Kevin Stone
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Hint
Only one of the ropes was exactly 33 feet.
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
Giving:
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
Double-Checking
Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99
Puzzle 152
Many years ago, a cruise liner sank in the middle of the Atlantic Ocean. The castaways luckily landed on a remote desert island.
There was enough food for the 135 people to last four weeks.
Nine days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 36 people stranded on the island to now share the original rationed food.
The food obviously had to be re-rationed, everyone was now on three-quarters of the original ration, so how many days in total would the food last, from the day of the original sinking?
Puzzle Copyright © Kevin Stone
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Hint
How many rations did they start with?
Answer
29 days.
Originally there was enough food for 135 people for 28 days, which totals 3780 rations.
After 9 days, 1215 rations had been eaten.
Therefore there were now 2565 rations left for 171 people, which would last for another 20 days at three-quarter rations per person = (2565 ÷ 3/4) / 171.
Which is 29 days in total from the original sinking.
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