Can you solve this?

That only works if you have a third container
Try this, call 5g container A, and 3g B
............................................A........... B
Fill A..................................5............0
pour from A to B........... 2...........3
empty B............................ 2...........0
pour from A to B............0 .......... 2
fill A....................................5.............2
pour from A to B...........4........... 3

Bathsheba

Good attempt, you were halfway there!

yggdrasil

Excellent!

The two methods of solving this puzzle, in terms of complements are:

a) 3 + 1 = 4, and
b) -1 + 5 = 4 (your method!)

Can you solve it by Method 'a'?

Alphabet Gestalt No. 2

If you put a vertical line through the letters on the top row they are mirror images of themselves

Haha, I missed the bit wbere it said using only two containers! I worked it out afterwards properly though.

Well spotted, Moneyboss!

Bathsheba
Did you have any joy with Method 'a' of 'Die Hard?

Erm, let's think how to explain my method....

Fill 3 gallon tin and pour into 5 gallon tin
Fill 3 gallon tin again and pour into 5 gallon tin till full (2 gallons)
This leaves 1 gallon in the 3 gallon tin
Empty 5 gallon tin
Pour the 1 gallon from the 3 gallon tin into the 5 gallon tin
Fill 3 gallon tin and pour into the 5 gallon tin, making 4 gallons in total in the 5 gallon tin.

Bathsheba

That's the one! Onto the next one?

I'm hoping other contributors will post more puzzles as I have a finite supply!

Here's today's puzzle!

Alphabet Gestalt No, 3

Why are some of the letters placed above the line, whilst others are below it!

AFGJLMNPQRSTUVWYZ
BCDEHIKOX

The ones below the line form a mirror image top to bottom, while the ones above the line don't.

Bathsheba

You're on fire with these puzzles!

Thus far, we've had algebra, electricity, water and gestalt!

So now let's try magnetism!

'Magnetic Attraction'
You are given two identical-looking pieces of mild steel, say 100 x 19 x 3mm (although the size is unimportant) and you are told that one of them has been magnetised, (forming a bar-magnet where one end has become a North Pole and the other end, a South Pole) whilst the other piece of steel is completely non-magnetised.

Your mission (should you decide to accept it!) is to identify which is which without using anything other than the two pieces of steel.

Stand one on end and balance the other on it. If it’s magnetised it should spin round to point due north.

Bathsheba

Principle is sound but in practice, owing to the Earth's magnetic field being so weak, it would be insufficient to overcome both the friction between the two pieces of steel and the inertia of the balanced piece.

In fact, (and assuming it was allowed in this problem) it would be unlikely to work if the magnetised sample was floated on a cork in a tub of water because of its inertia.

That's why in a plotting compass, the mass of the pointer is deliberately as low as possible and mounted on a simple gimbal to improve sensitivity.

A great attempt but I'm afraid it's back to the drawing board!

This is tricky. If the Earth's magnetic field is too weak to make one move, there must be a way of placing them asymmettrically , maybe in a T-shape? But I can't see how to tell .

I'll have a think about new puzzles next week, I like this thread:-)

yggdrasil

I can say that Earth's magnetic field has no bearing on a solution. The only solution that I'm aware of would work in space, far away from planetary magnetic fields and in zero gravity!

I eagerly await some new puzzles!

Whilst we're waiting for some new puzzles from forum contributors, here's a couple of easy examples to solve.

'A Counting'

The following is a list of the numbers 1 to 15 expressed in 4-bit binary code but they are not in sequential order.

0101 1110 1001 0010 1100

0111 1010 0011 1101 1000

0110 0001 1011 0100 1111

Can you identify which are the EVEN numbers in less than 10 seconds?



And for the second puzzle:

'Time on my hands'

'The B&B we stayed at last year had a chiming clock on the stairs. On the first night, I was having difficulty going off to sleep, when I heard the clock strike '1'.

After a while, as I tried to doze, I again heard the clock strike '1'.

Some time later still, I heard the clock strike '1' for the third time!

Assuming the clock wasn't faulty, what was the time when the clock struck '1' for the first time?'

Magnets: I think I was part way there.
Let first rod be A and second be B, Both perpendicular to each other. Bring the end of rod A to the middle of the other rod B (keeping both perpendicular to each other).
Now bring end of B to middle of A. if in first case there is attractive force but not in second case, it means B is magnetic. Because the polarity changes at the middle.
I must admit I did start googling, and found it was one of Martin Gardners. If this is your source of the puzzles, let me know, because I have two or three of his books somewhere which I haven't read for ages. :-)

Can you identify which are the EVEN numbers in less than 10 seconds? Yes. But then I can read binary :-)

And as for the clock, I guess the first chime was quarter past whatever hour you went to bed

And here's an easy one
The coloured socks

Ten red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?

yggdrasil

‘Magnetic Attraction’ Puzzle

You've got it!

Any permanent magnet exhibits a magnetic gradient from North Pole to South Pole with the centre region being essentially non-magnetic. This is more apparent in a bar magnet where the poles tend to be a significant distance apart compared to say, disc or ‘coin or other designs that result in the poles being relatively close together.

Consequently, by arranging the two pieces of steel in a T-form and the bar of the T (the horizontal component) happens to be the magnet, there will be a negligible force of attraction between the two pieces.

If, on the other hand, the branch of the T (the vertical component) is the magnet, there will be an easily discernible force of attraction between the two pieces.

I wasn't aware of Martin Gardner but I will look out for his books. My collection of puzzles hark back to the days when I was teaching.

Unfortunately or fortunately, depending upon your point of view, the internet will ultimately have the solutions to these puzzles. One of the challenges I faced was persuading students to 'have a go' themselves instead of the almost automatic resort to the internet for the answer!

The binary numbers puzzle originated from a true event when a lecturer spent some considerable time writing the binary equivalents of 1 - 31 on the board, before leaving the room. I think he expected the students to be kept busy with the problem until he returned some 15 minutes later!

With regard to the chiming clock, the answer I have is that since the clock was not a Westminster chime, it only sounded on the half-hour; consequently, the first strike would have been 00:30 but I could be wrong!

Probability was never my strong point! My initial reaction is to say 3 socks since if the first sock was red, the second could be blue, but the colour of the third sock doesn't matter since it will make a pair with either the red or the blue!

Socks puzzle.
The answer is 3.

Oh I did have a good go first, I got as far as the T-shape. But I was too intrigued not to look further. (And I did admit it)

So here is a more difficult one..........

Imagine that you are on a perfectly smooth sphere as big as the earth. A steel belt is stretched tightly around one of its equators.

One meter of steel (a little bit more than a yard) is added to this belt so that it is raised off the surface of the sphere by the same distance all the way around. Will this lift the belt high enough so that you can:
1) Slip a playing card under it?
2) Slip your hand under it?
3) Slip a baseball under it?

yggdrasil

I first encountered this problem in a different format; something to do with a cable running around the Earth on supports, but I like your scenario better!

One could be really cruel and introduce coefficient of expansion of the steel due to the effects of the sun but I think I may be going too far with that one!

I have the answer but don't want to deprive others from having a go first!

Here's a logical thinking puzzle called:

'To Cap It All'

There are four workmen and a tall wall!

One of the men stands facing the wall, whilst on the other side of the wall, the remaining three men stand in line, one behind the other but all facing the wall.

A slightly modified version of this puzzle appeared relatively recently on Dara O'Briain's TV show.

I am assuming there are 2 red and 2 green caps. If there could be a different number it can't be done I think

So 3 thinks: I can see 1 red and one green so I can't tell what mine is
2 thinks : I can see a red. If mine were red, 3 would know his is green, but he isn't saying anything so I will shout out mine is green!