# Brain Teasers are Back!

Thebadyogi stepped in with a brave attempt. His first three steps match the first three steps of Mrs D’s second solution. I therefore held back on posting either of Mrs D’s solutions.

I’ll hold off from posting either solution until later this evening …

To avoid the need to re-read half a dozen updates, i’ll simplify the text of the initial version of the teaser -

I have 3 jugs. One 8-pints; one 5-pints and one 3-pints.
The 8-pint jug is full of milk. the other two jugs are empty.
I want to end up with four pints of milk in the 8-pint jug and the other four pints of milk in the 5-pint jug.
I do this by pouring milk between these three jugs.
There are (at least) two ways of doing this.

I had to resort to pen and paper in the end, and worked out one solution in 8 steps, as follows:

1. 8/8 0/5 0/3
2. 3/8 5/5 0/3
3. 3/8 2/5 3/3
4. 6/8 2/5 0/3
5. 6/8 0/5 2/3
6. 1/8 5/5 2/3
7. 1/8 4/5 3/3
8. 4/8 4/5 0/3

Hopefully my notation makes sense/is followable.

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It makes perfect sense Bobby, and is the same as Mrs D’s second solution.
Well done !

PS I’m not surprised you had to resort to pen and paper

Well, just to close out the 3-jug teaser, both Mulberry and thebadyogi made good progress despite some misunderstanding of the words. And BobbyYork provided a perfect solution that matched Mrs D’s second demonstration.

So here is Mrs D’s first solution …

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… And here is Mrs D’s second solution, which matches that provided by Bobby, Well done Bobby !

When I wrote “… can be divided …” , I should have made it clear it means … “to give a whole-number answer, with no remainder”. eg 9 can be divide by 3 to give a whole-number answer. However, 9 can’t be divided by 4, you are left with a remainder.

A quick look would suggest immediately it can only be 2 or 3, as the others wouldn’t be divisible by 5.
Both of these would be divisible by 9 (as one of the multipliers is 45). However 56 also has 7 and 8 as factors, so Number 3 is my answer, ie 45 x 56.

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Well done Steve.

And very neatly explained.

The same as the answer to life, the universe and everything.

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Maybe if the great super computer “Earth” hadn’t been destroyed by the Vogons, that would have been the question it came up with?

Hang on, what if we are living on the Earth Mk2 and Don is the final conduit for the question? There’s a thought…

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Water, water, everywhere …

We had a picnic on Sunday, down by a babbling brook, or stream.

Mrs D needed exactly 6 pints of fresh stream water but realised she had only brought a 7-pint jug and a 5-pint jug.

She realised that she could fill jugs from the stream as often as she liked, and could return water to the stream as often as she liked. She could also pour water from one jug to the other as often as she liked. All she needed was 6 pints of stream water and all she had available to measure it was a 7-pint jug and a 5-pint jug.

I know how she did it. How would you do it ?

Mrs R said she would send me back because it was me that forgot to bring the 3 pint jug. Empty the milk into the 5 pint jug, then fill the now empty 3 pint jug with water and pour into the 7 pint jug. Repeat to get 6 pints of water.

Yes I know it’s not the right answer.

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Fill the 7, pour into the 5. 2 left in the 7.
Empty the 5, pour the 2 from the 7 into the 5
Fill the 7 again, then top up the 5, leaving 4 in the 7
Empty the 5 and pour in the 4 from the 7
Fill the 7 and top up the 5, leaving 6 in the 7

I think

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Well thought out badyogi. And very nicely explained.

Stagecoach

Anyone remember the classic film that appeared on our screens at Christmas all those years ago ?

Four horses galloping across the North American prairies with a four-wheel stagecoach in tow and a band of Indians in hot pursuit ?

The rear wheels were called “four-yarders” because that was the distance they would travel in one revolution – assuming no slipping or sliding! They also had 24 spokes per rear wheel. The front wheels were three quarters the diameter of the rear wheels, and only 12 spokes per wheel.

Sometimes the wheels appeared to be slowly turning backwards or slowly turning forwards. Well, the other evening, Mrs D and myself sat down with the DVD player to watch Stagecoach for old-times sake. Now, the notes on the DVD sleeve, made it clear that the manufacturing process had retained the authenticity of the original film which had been shot at 16 frames per second. So, we watched in anticipation to see which way the wheels on the stagecoach would appear to slowly turn! (sad really!)

We were sadly disappointed. During the first chase, there was no sign whatsoever of moving wheels. It wasn’t a very fast chase either, an Olympic sprinter could have run 100 yards faster!

However, to our surprise and delight, on the next two chases the wheels appeared to turn backwards, and then forwards as per the old movies !! success!!

“So,” I asked Mrs D “how fast was the stagecoach going in the first chase when there was no sign whatsoever of turning wheels?”

The ‘look’ that she gave me suggested she had better things to do such as decorating the dining room, winterizing the garden, washing her car ………

Perhaps someone on this forum could solve the speed of the stagecoach whilst I get started with the decorating !

Oh, the answer would be best in terms of yards per second.

I thought this little puzzle might keep a few grey cells ticking over whilst all the other grey cells are chasing the stagecoach

188
110,78
59,51,27
25,34,17,10
6,19,15,2,8

A neat little Pascal’s triangle - ie if the bottom numbers are A, B, C, D, E, the top number is A+4B+6C+4D+E

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Nicely done Steve.

And kudos for the Pascal’s triangle observation. Very nice !