Making Ends Meet Puzzle - Solution

Long-haired Mary Jones works for the Milk Marketing Board. 

Hairy Mary At The Dairy they call her. That's not very nice, is it? 

Anyway, Mary likes to eat her dinner by candlelight every evening. She saves all the candle ends because when she has collected seven ends, she can melt them down to make a new candle.

At the last count she found that she had 34 candles and 50 candle ends. One candle burns down in one evening. For how many evenings can Mary have a candlelit dinner before she has to buy more candles?

Clue: look at the title again!

Our Solution:

Mary has enough candles for 47 evenings. Let's see why:

34 candles last for 34 evenings, making 34 more ends. 
Add the 50 ends to make 84 ends, which is enough for exactly 12 new candles. (84 ÷ 7 = 12 remainder 0.) 

These 12 candles last for 12 evenings, making 12 ends. 
These 12 ends will make one new candle. (12 ÷ 7 = 1 remainder 5.) 

This candle lasts for 1 evening, making 1 end. We now have 6 ends left, so we do not have enough for any more candles.

Total: 34 + 12 + 1 = 47 evenings altogether.

Lemonink Puzzle - Solution

I have two glasses the same size. One contains 100 ml of lemonade and the other contains 100 ml of ink.



I take a spoonful of lemonade and stir it into the ink, and then take a spoonful of that mixture and stir it back into the lemonade. 

Which glass now contains least of the contents of the other one?

Our Solution:

The actual answer was that BOTH glasses contained the same amount of the other liquid in them. 

Each glass ends up with 100ml of liquid in it, as before, but the first glass (lemonade) has some of the lemonade replaced by ink, and this bit of lemonade can be found in the second glass (ink) where it is replacing the same amount of ink. Gettit?

Hourglasses 2 Puzzle - Solution

An eccentric professor used a unique way to measure time for a test lasting 15 minutes. 

He used just two hourglasses. One measured 7 minutes and the other 11 minutes. 

During the whole time he turned the hourglasses only 3 times. 

How did he measure the 15 minutes?

Our Solution:

When the test began, the professor started both hourglasses running. 

When the 7min hourglass ran out, he turned it around.

4 minutes later, the 11min hourglass ran out, and he promptly turned the 7min hourglass around again, so the 4 min ran back again.

11+4=15, and the test was over.



Footnote: Dr. J Sreedhar wrote to tell me that the Prof could have done it with one less flip:
* Start both (11-min and 7-min) hourglasses, but not the test.
* When the smaller one runs out, start the test. The bigger hourglass has 4 min to go.
* When the bigger hourglass also runs out, just flip it to measure out 11 more min.
* Test is over when the bigger hourglass runs out for the 2nd time.

Hourglasses 1 - Solution

You need to boil eggs for exactly 9 minutes, or else the visiting Duchess will complain, and you will lose your job as head chef.

But you have only 2 Hourglasses, one measures 7-minutes, and the other measures 4-minutes. How can you correctly measure 9 minutes?

The Solution . . .

Put the eggs on to boil and start both hourglasses running. 

When the 4-minute one runs out, turn it over immediately so it starts counting 4-minutes again

When the 7-minute one runs out, turn it over so it starts counting again

The moment the 4-minute one runs out for the second time, turn the 7-minute hourglass over - it will have only been running exactly one minute. 

Let the sand run back again (1 minute more) and then take the eggs off straight away, because they will have boiled for 9 minutes. 

(4 minutes twice, plus one more minute = 9 minutes!)

Hairytown - Solution

The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town

The town has now reached its maximum population - what is it?

The Solution . . .

There are 999 people in the town, from bald to 998 hairs.

Gurmit The Hermit Puzzle - Solution

Gurmit Burmit is a hermit - he lives all on his own on a lonely desert island. There is sand all around him: in front of him, behind him and on both sides, as far as Gurmit can see. In fact all he ever eats is sandwiches.

One day Gurmit decided to count the grains of sand. He started off by scooping up two handfuls of sand from the ground. "THERE MUST BE A BILLION GRAINS HERE IN MY HANDS" he thought to himself.

Was he close? Would his hands hold a billion grains of sand, or more, or less?

Our Solution:

A billion grains is an awful lot of sand.

The way to make estimates of large numbers like these is to build them up from smaller amounts by multiplying. 

First you can count 100 grains of sand and see how large a pile it makes. Put it in a teaspoon. Depending on how small the grains are you might find that 10 or 20 such small piles would fill a teaspoon.

So let us say that 2000 grains would fill a teaspoon.

Now let's imagine that Gurmit's hands will hold about 100 teaspoons of sand. 

That is only 200,000 grains!

A billion is 1,000,000,000 grains. Enough to cover Gurmit from head to foot!