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}

]]>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

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.

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

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!

]]>Nice puzzles, lot of fun to work on.

]]>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.

]]>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

]]>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