5-digit Number Puzzle

5-digit Number Puzzle - Solution
The Puzzle:
5-digit Number
What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.




Our Solution:
We can make an equation:

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857

The answer is 42857 (142857 is three times smaller than 428571)
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And Mint Sauce Puzzle

And Mint Sauce Puzzle - Solution
The Puzzle:
And Mint Sauce
Six wolves catch six lambs in six minutes.

How many wolves will be needed to catch sixty lambs in sixty minutes?

No, the answer is not sixty. Try again!




Our Solution:
I should also have said that the answer was not 10 either! That is a popular answer, but I'm afraid it is not correct. The right answer was SIX WOLVES.

Let's see why:

6 wolves catch 6 lambs in 6 minutes. Multiply by 10:
The same 6 wolves catch 60 lambs in 60 minutes.

(Give them 10 times as long and they'll catch 10 times as many lambs.)

Another way of seeing the answer is to note that each wolf catches 1 lamb in six minutes. In 60 minutes, therefore, each wolf will catch 10 lambs (ten times as many). With 6 wolves, six times as many lambs will be caught.
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How long will it take to fill the pool using all 4 taps at once

How long will it take to fill the pool using all 4 taps at once?
Our Solution:
First, work out how much of the pool gets filled by each tap in one hour.

The first tap takes 48 hours to fill the pool, so in one hour it fills 1/48 of the pool
The second tap 1/72
The third tap 1/96
And the fourth tap fills 1/6 of the pool

We need to add all those fractions together:

1/48 + 1/72 + 1/96 + 1/6 = 6/288 + 4/288 + 3/288 + 48/288 = 61/288

So, in one hour the pool will be 61/288 full

And it will be completely full in 288/61 hours = 4 hours 43 minutes and 17 seconds.
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Measuring Just 1 Liter Puzzle

Measuring Just 1 Liter Puzzle - Solution
The Puzzle:
Measuring Just 1 Liter
Imagine having three bowls, with the following capacities:

In bowl A (8 liters capacity) are 5 liters of water.
In bowl B (5 liters capacity) are 3 liters of water.
In bowl C (3 liters capacity) are 2 liters of water.

Can you measure exactly 1 liter, pouring only 2 times?




Our Solution:
Step 1. Pour from bowl A to bowl C until it is full - that only takes 1 liter.
So 4 liters are left in bowl A and bowl C is full (3 liters).

Step 2. Pour from bowl C to bowl B until it is full - that only takes 2 liters.
Bowl B is now full (5 liters) and there is 1 liter left in bowl C. Done.
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Measuring 7 Liters Puzzle - Solution

The Puzzle:

Jack and Jill did not have much success when they went up the hill to fetch a pail of water from the well. However, once they had both tumbled down the other side they found the pond and decided to get the water from there instead.



The problem was that they wanted 7 litres exactly. Jack's bucket held 5 litres and Jill's bucket held 3 litres. How did they bring back 7 litres? No guessing!

Our Solution:

One possible method follows:

1. Fill up the 5 litre bucket

2. Pour the 5 litre bucket into the 3 litre bucket until the 3 litre bucket is full.



3. Empty the 3 litre bucket.

4. Pour the remaining 2 litres from the 5 litre bucket into the 3 litre bucket.

5. Fill up the 5 litre bucket again.

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