Brain Teasers ? or 50 Years On........... ?

Don Atkinson posted:

.... my practise tests ......

Hopefully clear enough now! 

C.

Grandma is 80

You are 20 (if you say so!)

Christopher_M posted:

Don Atkinson posted:

.... my practise tests ......

Hopefully clear enough now! 

C.

sjbabbey posted:

Grandma is 80

You are 20 (if you say so!)

I do say so..................

I think I should have changed the wording to reflect the circumstances today as opposed to 60 years ago !!!

Just to confirm for those who have tried the above 4-minute test of mental arithmetic..........

SJ has it with 80 and 20.

D 4/7 is the middle fraction

C 2 both Nine and Eleven make the sentence true

C  45 x 54 is the only product divisible by the numbers 1 to 10 inclusive

Oh ! and many thanks to Chris for drawing attention to my atrocious spelling. 3/20 was my typical score in spelling tests..............."Atkinson !" my English teacher used to shout "you are not just the worst speller in this school, you are the worst speller this school has ever had !" She was even less complimentary about my grammar, and it was an error in grammar that produced practise.........

Browsing through my "O"-Level book this evening I came across the following mental maths problem :-

Which is the larger value:-  √225 + √64   or   √(225 + 64)   ?

Ok, none too difficult even doing it "in your head"............and "nice, satisfying numbers"

But then I realised that √144 + √25   verses   √(144 + 25) also had "nice, satisfying numbers"

As did √16 + √9   verses   √(16 + 9) have "nice, satisfying numbers"

And a pattern began to emerge because (for example) √25 + √16   verses   √(25 + 16) didn't have "nice, satisfying numbers"

I am wondering if this "pattern" is a definite pattern for even larger combinations than √225 and √64 ?  (assuming that there are larger combinations with the same properties ?

Anyway, I hope that you also find the above three examples "nice, satisfying numbers" ?

Golf - The Masters has just finished so...............

A factory making golf balls stacks 10,000 of them in several layers.

The top layer has a single row of balls, the second layer has two rows, the third layer has three rows, and so on.

Second layer rows each have one more ball than the top layer row, third layer rows each have two more balls than the top layer row and so on.

Of the several possible shapes of the stack, the one used takes up the smallest floor area.

How many balls are in its bottom layer?

Masters Golf puzzle:-

I think the bottom layer contains 24 rows of 41 balls = 984 balls in total.

(Does resorting to Excel incur a 2 shot penalty....?)

Steve D

steved posted:

Masters Golf puzzle:-

I think the bottom layer contains 24 rows of 41 balls = 984 balls in total.

(Does resorting to Excel incur a 2 shot penalty....?)

Steve D

A 2-shot penalty ? more like a hole-in-one Steve

I'm have to admit to resorting to Excel, although I did start off with :-

• b= balls in top row
• n = number of rows
• g = number of golf balls in total
• g = b + 2(b+1) + 3(b+2).....n(b + n - 1) = 10,000   which led to :
• b = (60,000 - 2n³ + 2n) ÷ 3(n² + n)
• after which I used Excel for successive numbers of "n"

In the past couple of days, the Gov has indicated the possibility of new Grammar Schools, up from the current 163. Although I doubt we will see the numbers increase to 1,500 + of the 1960's I understand that selection would by means of an 11+ exam.

I recalled my 11+ of c. 60 years ago............a few maths questions and a bit of English comprehension. So I thought i'd have a quick peak at a couple of sample questions from current 11+ exams, just to see how much easier they would be these days. Well, standards have dropped remarkably, haven't they !!!!

Here is the first one I read............

Marco, Laura, Peter, Ben and Sally are out shopping for jackets. Ben and Laura want waterproof jackets, Peter and Sally want brightly coloured jackets with hoods, Laura and Marco want lightweight jackets and Marco and Ben want brightly coloured jackets but with a warm lining.

Out of the following statements, which one must be true?

A. Sally and Peter want different types of jackets.

B. Only two people do not want brightly coloured jackets.

C. No one wants a lightweight jacket with a hood.

D. Sally wants a coat with a hood and a warm lining.

E. Four of them do not want waterproofs.

..............and the second question I encountered............

Select the option (A, B, C or D) which has the sentence with the most suitable grammar

1. Was it he whom had a house burn down?
2. Was it he whose house burnt down?
3. Was it he that had a house burn down?
4. Was it he who's house burnt down?

An infinitely large floor is covered with hexagonal tiles of side L. Different colours of tiles are used so that no two touching tiles are the same colour.

A thin hoop of diameter d  is thrown onto the tiles. What is the probability that the hoop encloses more than one colour ?

Apologies for the rough diagram, the hexagonal tiles are all intended to just touch one another along sides length L. It would take too much effort in Power-point to adjust the position of each tile accurately !! Also, the question makes it clear that adjacent tiles are different colours. I have drawn them all blue, again this is a short-cut by me !

Don Atkinson posted:

In the past couple of days, the Gov has indicated the possibility of new Grammar Schools, up from the current 163. Although I doubt we will see the numbers increase to 1,500 + of the 1960's I understand that selection would by means of an 11+ exam.

I recalled my 11+ of c. 60 years ago............a few maths questions and a bit of English comprehension. So I thought i'd have a quick peak at a couple of sample questions from current 11+ exams, just to see how much easier they would be these days. Well, standards have dropped remarkably, haven't they !!!!

Here is the first one I read............

Marco, Laura, Peter, Ben and Sally are out shopping for jackets. Ben and Laura want waterproof jackets, Peter and Sally want brightly coloured jackets with hoods, Laura and Marco want lightweight jackets and Marco and Ben want brightly coloured jackets but with a warm lining.

Out of the following statements, which one must be true?

A. Sally and Peter want different types of jackets.

B. Only two people do not want brightly coloured jackets.

C. No one wants a lightweight jacket with a hood.

D. Sally wants a coat with a hood and a warm lining.

E. Four of them do not want waterproofs.

Hi, 

I think answer C is true.

From what I can gather, Peter and Sally want the same jackets. Four of the five want bright colors. Two want waterproof jackets, which leaves only three who may not want waterproofs. Therefore answers A, B and E cannot be true.

If my vocabulary is good enough, a coat is not the same as a jacket, which would then rule out answer D.

Don Atkinson posted:

In the past couple of days, the Gov has indicated the possibility of new Grammar Schools, up from the current 163.

With all these teasers, Don, you're a shoo-in for the headmaster at St Theresa's GS.

Best, C.

Hi Mulberry, Spot-on with answer C.

But even if we took a "coat" to mean a "jacket" (I agree with you the two are different things) but even so, Sally only specified a "hood" and "bright colour", no mention of a "warm lining".

But well done. Clearly potential Grammar School material

FWIW, I considered some of the sample questions to be worded ambiguously.

Christopher_M posted:

Don Atkinson posted:

In the past couple of days, the Gov has indicated the possibility of new Grammar Schools, up from the current 163.

With all these teasers, Don, you're a shoo-in for the headmaster at St Theresa's GS.

Best, C.

Ha, Ha. My 9 year-old grandson thinks the same, but for different and not entirely flattering, reasons !!!!

Don Atkinson posted:

In the past couple of days, the Gov has indicated the possibility of new Grammar Schools, up from the current 163. Although I doubt we will see the numbers increase to 1,500 + of the 1960's I understand that selection would by means of an 11+ exam.

I recalled my 11+ of c. 60 years ago............a few maths questions and a bit of English comprehension. So I thought i'd have a quick peak at a couple of sample questions from current 11+ exams, just to see how much easier they would be these days. Well, standards have dropped remarkably, haven't they !!!!

Here is the first one I read............

Marco, Laura, Peter, Ben and Sally are out shopping for jackets. Ben and Laura want waterproof jackets, Peter and Sally want brightly coloured jackets with hoods, Laura and Marco want lightweight jackets and Marco and Ben want brightly coloured jackets but with a warm lining.

Out of the following statements, which one must be true?

A. Sally and Peter want different types of jackets.

B. Only two people do not want brightly coloured jackets.

C. No one wants a lightweight jacket with a hood.

D. Sally wants a coat with a hood and a warm lining.

E. Four of them do not want waterproofs.

The answer is none. (None of them MUST be true):

A. The only information given about Sally and Peter's wants is the same

B. Peter, Sally, Marco & Ben all want bright?

C. Not enough information is given to know this: the fact that hoods aren't mentioned deosn't mean they haven't got hoods.

D. Not enough information to know this: Sally wants a jacket with a hood, but we are not told if it has a warm lining (this is aside from whether a jacket is a coat - which would make this answer negative as she wanted a jacket)

E. Not true as 2 want waterproofs so at most 3 don't.

IB, you have a point. Quite a good point IMHO. Some of these questions do seem to be open to discussion as to their meaning.

If (ha ha !!) the question had made a positive statement that it contained ALL the relevant facts about each person's wants (= specific specification) and also substituted "specified" for "wants" in the question and answers, perhaps we could live with answer C ??

BTW, I copied the questions word for word. I'm not sure how an appeal to the Exam Board would go. Not very well, would be my guess. But you could try........

Don Atkinson posted:

IB, you have a point. Quite a good point IMHO. Some of these questions do seem to be open to discussion as to their meaning.

If (ha ha !!) the question had made a positive statement that it contained ALL the relevant facts about each person's wants (= specific specification) and also substituted "specified" for "wants" in the question and answers, perhaps we could live with answer C ??

BTW, I copied the questions word for word. I'm not sure how an appeal to the Exam Board would go. Not very well, would be my guess. But you could try........

Imprecise questions are a serious problem, and really I think exam boards need to be more thorough in reading what the questions actually say, not what they mean it to say. One I recall from many years ago, though I don't remember at what level, was a simple mechanics one:

With a shelf mounted on a wall using a bracket as shown in the provided diagram, at which point is the force pulling on the screw holding it to the wall greatest, A or B

The diagram showed a standard inverted 'L' shaped bracket, with A marked near the top of the vertical part of the bracket just below the shelf, and B marked near the bottom of the bracket, 

It didn't state whether there was only the one screw, or one at each position. I took the question to mean just a single screw, and answered B. The declared correct answer was A.

Don Atkinson posted:

..............and the second question I encountered............

Select the option (A, B, C or D) which has the sentence with the most suitable grammar

1. Was it he whom had a house burn down?
2. Was it he whose house burnt down?
3. Was it he that had a house burn down?
4. Was it he who's house burnt down?

B

this reminds me of an 11-plus question someone a few years older than me told me about some time ago, so from late 1950s:

Punctuate the following so that it is grammatically correct and makes complete sense:

     time flies you cannot they fly at such irregular intervals

Innocent Bystander posted:

Imprecise questions are a serious problem, and really I think exam boards need to be more thorough in reading what the questions actually say, not what they mean it to say.  

Very true, as I noticed when some of my students gave very well reasoned answers to some of my questions, which were not at all what I thought they should be. Fortunately most answers were the "right" ones and it was in preparation for the exams.

Innocent Bystander posted:

Don Atkinson posted:

..............and the second question I encountered............

Select the option (A, B, C or D) which has the sentence with the most suitable grammar

1. Was it he whom had a house burn down?
2. Was it he whose house burnt down?
3. Was it he that had a house burn down?
4. Was it he who's house burnt down?

B

this reminds me of an 11-plus question someone a few years older than me told me about some time ago, so from late 1950s:

Punctuate the following so that it is grammatically correct and makes complete sense:

     time flies you cannot they fly at such irregular intervals

I'm not sure that I can detect any form of punctuation that would make complete sense of that string of words !!

Time flies ? You cannot ! They fly at such irregular intervals !

That's the best I can do at the moment, and it doesn't make much sense, if any, even to me !

Even worse than "eats shoots and leaves"....................

The hexagonal question above isn't too difficult.

Especially if you look back to page 3 of this thread !

Don Atkinson posted:

 

Innocent Bystander posted:

Don Atkinson posted:

..............and the second question I encountered............

Select the option (A, B, C or D) which has the sentence with the most suitable grammar

1. Was it he whom had a house burn down?
2. Was it he whose house burnt down?
3. Was it he that had a house burn down?
4. Was it he who's house burnt down?

B

this reminds me of an 11-plus question someone a few years older than me told me about some time ago, so from late 1950s:

Punctuate the following so that it is grammatically correct and makes complete sense:

     time flies you cannot they fly at such irregular intervals

I'm not sure that I can detect any form of punctuation that would make complete sense of that string of words !!

Time flies ? You cannot ! They fly at such irregular intervals !

That's the best I can do at the moment, and it doesn't make much sense, if any, even to me !

 

That is the correct answer (ignoring the gaps before the question and exclamation marks).

And it does make complete sense to me, as an answer to an unspoken request or challenge by someone to time some aspect of flies' behaviour.

Adults tend to find this question more difficult than children, because by adulthood the meaning of time flies as in tempus fugit tends to come to mind first, whereas a 10-11 year old child might more readily think of timing as in races.

Which of the circles in the maze is closest to the Exit ? (all the rectangles are squares and are equal)