# Brain Teasers are Back!

#41

Hi Ian,

I did the maths. It seemed easy enough and it was.

Nonetheless, I was a bit surprised to find the relative speeds at impact were the speeds that the brick would achieve when traversing the passing point of the lifts, + or - the speed of the lift.

For some reason, I imagined the brick might take longer to catch the down-going lift and that its speed would be relatively high.

Nice one !

#42

Yes ! no easy-to-solve equation. Just a grubby little “equality” to enable successive guesses. But Excel makes the guessing relatively painless.

I pushed on a few more decimals to 1.15872847 times the radius of the field.

#43

Nobody seems to have tackled the “Fulcrum” at post #18 above.

It’s not difficult, so I can imagine some might think there’s a “catch” (there isn’t !)

Other’s might think it’s so easy it’s beneath them … well, ok ! (but I do try to find a wide range of teasers from the sublime to the rediculous !)

#44

So, in addition to the “Fulcrum” which is basically geometry, I thought somebody might like a “Probability” challenge. But not too difficult !

I am considering a wager.
Which of the following three dice rolls has the greatest probability of winning ?

Throwing 6 dice and getting at least one six
Throwing 12 dice and getting at least two sixes
Throwing 18 dice and getting at least three sixes

And as a supplement, what are the various probabilities ?

#45

And for those with an interest in slightly more challenging geometry…

This puzzle is called Kou Ku, derived from the names given to the two sides that form a right angle triangle. In English they mean thigh and leg. The hypotenuse is called Hsein, or lute string.

The puzzle requires you to discover the size of the largest square that can fit inside a right angle triangle, making use of the pre-existing right angle as illustrated.

There is a right angle triangle with Kou of 5 ch’ih and Ku of 12 ch’ih. How many ch’ih is the largest square that can fit inside.

#46

Keep the easy ones coming.

I think the fulcrum volume is 56

#47

Hi Fatcat,

I think you’re right with 56. Well done !

There have to be one or two difficult ones - well, to me they have to seem difficult, you guys usually eat them up faster than I can type them

Cheers, Don

#48

The view of this problem without any maths is nice too. Instead to thinking about the lifts moving up and down, imagine the scenario from the frame of reference of the lift. In that frame the lift is always stationary, and the two cases correspond to the brick having either an upward or downward initial velocity of v (the same speed as the lifts in the original question). Consider first the brick with the initial downward velocity - it will accelerate from v to some higher speed until it hits the lift. The brick with the initial upward velocity of v first rises and decelerates then begins to fall because of gravity. At the instant it has fallen back to its initial height its speed is again v but now in the downward direction. So what happens thereafter is exactly the same as happened to the other brick. So both bricks hit the elevator with the same relative velocity and inflict the same damage. Remember the lift is stationary in this picture.

#49

But this analysis is only valid if the lifts are at the same elevation when the brick starts to fall. That boundary condition was not specified in the original question.

If you do the analysis on the basis of the two lifts being at the same height when the brick hits, you get my original answer - always more damage for the lift going up.

#50

Sorry if what I wrote wasn’t clear - Don had some queries about to too so I guess I could have made it more explicit.

Yes, if an upward and downward moving lift were to be struck at the same height the upward one would have a greater relative velocity and sustain more damage as you say.

#51

No need for an apology - it is interesting that the solution depends so much on the boundary conditions!

#52

Hi Ian, Hi Dozey,

I agree that Ian’s initial wording was somewhat vague and I had difficulty figuring out why he expressed such surprise at the outcome when he had first seen this puzzle, presumably a few years ago.

That is why I sought clarification of the postulated situation. You can see from my abstracted quotes that I was unsure whether the brick dropped as the lifts passed each other, or did the bricks drop so as to hit the lifts as they passed each other. Fortunately Ian clarified his wording and I was then (and only then) able to understand what he was after.

I think this illustrates how difficult it sometimes is to get the wording of these Brain Teasers exactly right. And why I have had to apologise quite a few times in the past !!

#53

The first part of the “dicey” puzzle isn’t difficult.

The option to work out the actual probabilities is a bit more challenging

#54

I don’t do these brain teasers normally, but this one was sent to me. What answer do you get and approximately how long did it take for you to get it?

#55

I believe this question was tackled in the “barmaid’s brain”, with the answer being: when you run you get wetter …

#56

860 or -148 I think. Took about 5 minutes.

#57

The same as Eoink ie 860 or -148. Also about 5 mins.

I also reckon a few people might come up with 80 or 720 if they fail to do the multiplication element first.

The values I get for the various brick walls are :-
(20; 12; and 8) giving -148 and
(36; -4; and -24) giving 860

#58

I got -148 in about the same time and promptly put my result in a bit of fun completion set up by someone. They then announced the winner as 80 and said mine was wrong. Clearly they are saying the multiplication of 8x20 doesn’t come first.

#59

Hi Count.d,

Your -148 was correct. The competition organisers were wrong.

Reminds me of that childish tormentor … “Constantinople is a very big word, but if you can’t spell it, you must be a dunce”. The tormentor waits for you to struggle through various versions of Constantinople, all of which you get wrong, even though some of your spellings are correct. He then triumphantly announces that “it” is spelt “I…T”.

There is a well established hierarchy of arithmetic operators. Multiplication and division always take place before addition and subtraction.

The only way to arrive at 80, would be to group the first two terms within a set of brackets. Not easy with the pictures of bricks.

#60

My workings.
I put the (missing) brackets in at the bottom (as I often do), just to remind myself the order of arithmetic.