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## #1 2012-09-14 23:52:01

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### New Puzzles 1

I am adding a lot of new puzzles by Stephen Froggatt (a retired teacher). Here is the first batch.

Have fun, and let me know how you got on (and if you find anything amiss) ... !

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #2 2012-09-15 00:38:23

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: New Puzzles 1

Hi MIF

I like those. The hermit puzzle is classical Fermi question.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2012-09-15 00:38:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: New Puzzles 1

Hi MIF;

Circling the square problem I believe is correct. Would you consider mentioning that geogebra can create these shapes and make this problem easier to solve than by cutting.

In the solution you might try putting a picture of the answer which makes a convincing display.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #4 2012-09-15 00:51:17

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: New Puzzles 1

Oh, btw, if matchsticks are of the same length then the solution to that puzzle is incorrect!

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #5 2012-09-15 01:02:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: New Puzzles 1

Hi;

In the Path Plodding Puzzle another route is

start, finish, F, C, G, start, C, B, A, D,F,E,A, finish.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #6 2012-09-15 10:08:59

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: New Puzzles 1

Wonderful. Included your circles diagram, bobby, and mentioned GeoGebra, thanks. And included your Path Plodding Puzzle solution.

Also mentioned matches don't have to be same length, thanks anonimnystefy.

Will post more puzzles when I can.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #7 2012-09-15 10:16:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: New Puzzles 1

Hi MIF;

Thanks, those are very nice puzzles.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #8 2012-09-25 10:37:59

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: New Puzzles 1

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #9 2012-09-25 12:46:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: New Puzzles 1

Hi MathsIsFun;

For the "Sticker-bility" puzzle your help solution is correct and there is only one solution to it.

But if you did not give any help then there are 74 solutions to the puzzle below. In case someone mentions that.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #10 2012-09-25 18:59:53

bob bundy
Registered: 2010-06-20
Posts: 8,228

### Re: New Puzzles 1

hi MathsIsFun,

Thanks for the puzzles.  I'm still working through.

I've got to "It Must Be Matchic Puzzle"

Couldn't you have six equal matches in a tetrahedral format ?

"Hilda the Builder"

You could re-word this to ask for the least number of bricks.  That way, just one answer.

But

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #11 2012-09-26 10:34:46

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: New Puzzles 1

Thanks bobby and bob.

(Don't leave us in suspense bob, "But...")

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #12 2012-09-26 18:44:37

bob bundy
Registered: 2010-06-20
Posts: 8,228

### Re: New Puzzles 1

hi MathsIsFun,

(Don't leave us in suspense bob, "But...")

???

Sorry, but what are you awaiting?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #13 2012-09-27 01:18:30

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: New Puzzles 1

Hi MIF

I like the second batch as well.

Hi Bob

Both solutions to the Matchic puzzle seem acceptable, but only with that wording and solution is it an original puzzle.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #14 2017-10-11 09:29:30

RVave
Member
Registered: 2017-10-11
Posts: 1

### Re: New Puzzles 1

In response to the Lemonink puzzle: I believe that the lemon glass will contain less ink than the ink glass will contain lemon. The following is based on two assumptions: the amount taken out of each glass is 10 mL and that the amount taken is allowed to mix thoroughly in the glass. Assuming that the lemon transferred to the ink glass will mix into the ink, only part of the lemon will be returned to the lemon glass and some of the ink transferred to the lemon glass will contain some lemon in it. If the lemon transferred to the ink glass is thoroughly mixed into the ink before the same amount is taken out of the ink glass and transferred back to the lemon glass there will be 99.0909...% lemon in the lemon glass with the rest being ink, and there will be 90.909...% ink in the ink glass with the rest being lemon. The only way that the amount of lemon in one glass could equal exactly the amount of ink in the other glass would be if somehow one avoided taking any lemon back to the lemon glass while collecting ink out of the ink glass. If the assumption about the quantity is not taken, there is another way that the amount of lemon in each glass could equal the amount of ink in the other glass; that is if instead of a spoonful the amount taken from the lemon glass was exactly half (50mL). Depending on the size of the spoonful, the lemon glass will always contain less ink than the ink glass does lemon up to the point that the spoon is half of the glass. I would not assume a spoonful to contain 50mL or more, but if the spoon were to hold more than 50mL then the converse would be true, the ink glass would contain less lemon than the lemon glass did ink after the transferring of the quantities from each glass.

Let me know what you think, and how I could have said this more clearly. I am sure that there must be a simply beautiful way to say this in "Math Speak", unless of course I am just wrong.

Last edited by RVave (2017-10-11 11:03:13)

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## #15 2017-10-11 21:01:06

bob bundy
Registered: 2010-06-20
Posts: 8,228

### Re: New Puzzles 1

hi RVave

Welcome to the forum.

Some puzzlers like to make a simple thing complicated just to make it hard.  The "As I was going to St Ives" puzzle is an example.

So is Lemonink.

The amount transferred is irrelevant.  Let's say we have a glass with 100mL lemonade and a second with 100mL of ink.

Start tipping liquid from one to the other in any way you like and as many transfers as you like. Stop when the first glass has exactly 100mL of liquid in some mixture.  There's no way we can know how much is lemonade so let's say it has x mL of lemonade.  As it has 100 altogether there must be 100 - x mL of ink.

The second glass must also have 100mL altogether as long as we didn't spill or drink (!) any.  How much is lemonade?  Well we know where x units is so the second glass must have 100 - x mL of lemonade.  And as there are 100mL altogether in that glass there must be x mL of ink.

So in the first glass lemonade : ink = x : 100-x and in the second ink : lemonade = x : 100 -x

I did read your explanation, but I got totally lost half way through.  Sorry.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #16 2017-10-21 19:35:40

sztoian
Member
Registered: 2017-10-21
Posts: 1

### Re: New Puzzles 1

I'm new here (not new to math) and I got a different answer to only the second puzzle I encountered, "Making Ends Meet".  Your answer (or Steve Froggatt's) seems to me to "make a simple thing complicated"...  Why not add up all the possible whole candles, 34 + (50/7) = 41-1/7 or 41.142857, then multiply by 7/6ths [getting total qty of ends, then dividing by the usage rate per candle].  This yields 48 candles.  Of course, on the last evening, with the only slightly shorter candle, she will have to eat a little faster, skip dessert, or let the candle burn right to the end!

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