Brain Teasers - good ones!

My advice when trying to solve brain teasers is to attack them using the scientific method. Therefore, following in the footsteps of Karl Popper and Richard Feynman propose bold conjectures but be sure to test them under several conditions, especially under bizarre conditions.

Do not try them all at once; try one at a time.

This is a particularly good one:

There are 2 pieces of string. Each piece is made of a different material and they are of different lengths. Both pieces of string take exactly 1 hour to burn from one end to the other end. The speed of burning is not uniform throughout, so they can burn quickly first, then slowly at the end or in any random way. If you are given only these 2 pieces of string and a box of matches, how do you measure 45 minutes?

The solution only requires you to burn the strings. No other actions like cutting, measuring, folding etc. is involved.

Hint: I will leave you to set up your own bold conjectures but as for bizarre conditions, how about assuming that one of the strings burns 90% of its length in just 5 minutes, while it takes 55 minutes to burn the remaining 10%.
Reject any solution which will not work under this 'bizarre' condition.

This is to show you that your computer can read your mind.

It is very impressive, that is, until you see how it is done!   Click    here    to have a go.

An interesting problem I found tbe tbe New Scientist.

A VERY well known software house gives the following question to prospective employees. They expect them to solve it in less than 5 minutes. I must be losing my touch; it took me a somewhat longer!

"U2" has a concert that starts in 17 minutes and all band members must cross a bridge to get there.

All four men begin on the same side of the bridge.

You must organize them so that they all cross to the other side in time. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:

Bono: - takes 1 minute to cross
Edge: - takes 2 minutes to cross
Adam: - takes 5 minutes to cross
Larry: - takes 10 minutes to cross

For example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have elapsed and you have failed the mission.

Notes: Once again, there is no trick. It is the simple movement of resources in the appropriate order. There are two known answers.

This one has been around since I was a lad. It is a good one nevertheless:

You have 12 billiard balls: they all weigh the same except for one. You have a two pan beam balance BUT you are only allowed three weighings.

You are required to identify the odd ball and to say whether it is heavier or lighter than the others.

This one beat me and I had to ask for help!

The Cheating Husbands.

Once upon a time there was a matriarchal city.
The women had to pass a logic exam before they were allowed to marry.
The Queen was known to be absolutely truthful.
The women were obedient to the queen.
The city was so small that every women heard every gun shot fired in the city.

One Saturday afternoon all the women gathered in the City Square.
The Queen read the following:
There are one or more unfaithful husbands in this city.
Although none of you knew before this gathering whether your own husband is faithful, each of you does know which of the other husbands are unfaithful.
I forbid you to discuss what I have just told you.
Should you discover that your husband is unfaithful, you must shoot him at midnight on the day you make the discovery.

The women all went home and started to think........

No shots were heard that night, nor for the next few nights, but on Thursday night at midnight a volley of shots was heard.

QUESTION:

How many cheating husbands were shot at midnight on Thursday and how many got away with it?

I was not going to let this one beat me but I must confess that it took me three weeks - it's a beauty!

23 Prisoners.

A warden meets with the 23 prisoners when they arrive at the prison. He tells them:

You may meet together today and plan a strategy, but after today you will be in isolated cells and have no communication with one another.

There is in this prison a "switch room" which contains two light switches, labelled "A" and "B", each of which can be in the "on" or "off" position. I am not telling you their present positions. The switches are not connected to any appliance. After today, from time to time, whenever I feel so inclined, I will select one prisoner at random and escort him to the "switch room". This prisoner must select one of the two switches and reverse its position (e.g. if it was "on", he will turn it "off"). The prisoner will then be led back to his cell. Apart from these prisoner visits no one will ever enter the "switch room".

At any time, any one of you may declare to me, "We have all visited the switch room." If it is true (ie. each of the 23 prisoners has visited the switch room at least once), then you will all be set free. If it is false (someone has not yet visited the switch room), you will all remain here forever, with no chance of parole.

Devise a strategy which will guarantee the prisoners' release.

Do not give up on any of these without trying very hard, but if desperate,
-email: Tony Heyes

Now some things I find amusing......

 

 

 

Now look at the spinning young lady.
Sometimes you see her turning to the right and sometimes to the left.
A great example of a Gestalt phenomena.

For me she almost always turns to the right but I can look at the shadow of the feet and "make" her go the other way!

 

 

 

 

Now read this from Cambridge University .

Olny srmat poelpe can raed tihs. I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh? yaeh and I awlyas tghuhot slpeling was ipmorantt! if you can raed tihs psas it on !!

Or try this one .... .

F1gur471v3ly 5p34k1ng?
7H15 M3554G3 53RV35 7O PR0V3 H0W 0UR M1ND5 C4N D0 4M4Z1NG 7H1NG5! 1MPR3551V3 7H1NG5! 1N 7H3 B3G1NN1NG 17 WA5 H4RD BU7 N0W, 0N 7H15 LIN3 Y0UR M1ND 1S R34D1NG 17 4U70M471C4LLY W17H 0U7 3V3N 7H1NK1NG 4B0U7 17, B3 PROUD! 0NLY C3R741N P30PL3 C4N R3AD 7H15. PL3453 F0RW4RD 1F U C4N R34D 7H15.

For a splendid collection of mind stretching puzzles visit Nick's Mathematical Puzzles

 

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