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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,640

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

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,030

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

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,752

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

**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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,640

anonimnystefy wrote:

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.

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,752

Hi MIF;

Nice puzzles, lot of fun to work on.

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,030

MathsIsFun wrote:

anonimnystefy wrote: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!

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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**konop****Member**- Registered: 2017-01-21
- Posts: 1

Solution to "The Schoolgirl Problem" is wrong.

Wed BEG and Sat BDG - so B and G met 2 times.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,752

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.

**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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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,051

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 are**7**number of ways.

**{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.}**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,752

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}

**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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