Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

New Puzzles 5

Yet more ...

It Could Be Verse
Measuring 7 Liters
Mince Pie Madness
Santa Has A Bad Code
Four-sided Dice
The Schoolgirl Problem
The Pearl Necklace
One Square and a Half
Missing Number 1
Squares on a Chess Board
Alphabet Numbers
Ten Coins in Five Rows

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: New Puzzles 5

I disagree with the number alphabet puzzle's solution. You can write myriad with the letters.

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: New Puzzles 5

Hi MIF;

For the "It Could Be Verse" puzzle there are three more solutions:

For "Mince Pie Madness" that is the correct solution. You solve it using this equation.

p = 109

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: New Puzzles 5

I disagree with the number alphabet puzzle's solution. You can write myriad with the letters.

Nice! Also "many", "lots" and "heaps".

Thanks bobby for those, will add them.

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: New Puzzles 5

Hi MIF;

Nice puzzles, lot of fun to work on.

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: New Puzzles 5

I disagree with the number alphabet puzzle's solution. You can write myriad with the letters.

Nice! Also "many", "lots" and "heaps".

Thanks bobby for those, will add them.

Well, unlike "heaps" and "many" and such, "myriad" is an actual number.

The puzzles are nice indeed! And there have been so many new ones in the last couple of days! Keep up the good work!

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“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.

konop

Member

Registered: 2017-01-21

Posts: 1

Re: New Puzzles 5

Solution to "The Schoolgirl Problem" is wrong.
Wed BEG and Sat BDG - so B and G met 2 times.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: New Puzzles 5

Hi;

Here is one solution:

https://en.wikipedia.org/wiki/Kirkman%2 … rl_problem

I have translated it to letters hoping I did not make a mistake.

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: New Puzzles 5

There is a nice analytical approach to the "It could be verse"problem.
If a and  b be the number of two types of cake. 30a+40b=850 or 3a+4b=85
we can consider a packet of 12. Each packet can be distributed as four 3s or three 4s.In 85 there are 12 packets and 1 is left out. The remainder can not be distributed into 3s and/or 4s.So we open one pack ,add to the remainder to make it 13 which is three 3s and one 4.So there are 6 packets left out.We can distribute any number of packets varying from 0 to 6 (in 7 ways) to 3s and the remaing to 4s. thus there are7number of ways.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: New Puzzles 5

Or if you do not want to utilize combinatoric reasoning and wish to apply the teakettle principle you can use the generating function:

Looks formidable, math notation is rather clumsy and seems to be designed to confuse rather than enlighten, but it is easy to solve computationally. We check the coefficient of x^85 and find that is 7, meaning there are 7 solutions to this.

We can also use Bezouts Identity:

From the first solution (27,1) this reduces to

now we only have to apply k = 0, -1, -2, -3, -4, ... to get all the solutions:

{3, 19}, {7,16}, {11, 13}, {15, 10}, {19, 7}, {23, 4}, {27,1}

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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.