Newspaper puzzle

In a poll of mindset solvers,exactly two - sevenths said they liked question 1 best:an exact number of fifths(more than none)said they liked question 2 best;700 said they liked question 3 best.How many were polled

@venda

2p/7 + xp/5 + 700 = p

x and p are integers

solve for p:
  10p + 7xp + 24500 = 35p
  7xp + 24500 = 25p
  25p - 7xp = 24500
  (25 - 7x)p = 24500
  p = 24500 / (25 - 7x)

prime factors of 24500:
  2*2*5*5*5*7*7 = 24500

if x = 1, the denominator is 18; 18 is not a factor of 24500
if x = 2, the denominator is 11; also not a factor
if x = 3, the denominator is 4; this IS a factor
if x >= 4, the denominator is negative, leading to negative people polled

x = 3, p = 6125

@bigdogg said
@venda

2p/7 + xp/5 + 700 = p

x and p are integers

solve for p:
  10p + 7xp + 24500 = 35p
  7xp + 24500 = 25p
  25p - 7xp = 24500
  (25 - 7x)p = 24500
  p = 24500 / (25 - 7x)

prime factors of 24500:
  2*2*5*5*5*7*7 = 24500

if x = 1, the denominator is 18; 18 is not a factor of 24500
if x = 2, the denominator is 11; also not a factor
if x = 3, the denomin ...[text shortened]... factor
if x >= 4, the denominator is negative, leading to negative people polled

x = 3, p = 6125

Must be a first!
No mention of 700 in this weeks puzzle:-
The three kings bought gifts of gold frankincense and myrrh, but forgot to agree who would bring what.Caspar and Melchior both bought one at random.Balthazar bought 2(hoping to re-gift the other)What are the chances that each king was able to present a different gift

@venda

It's that season 😉

So the probability that Caspar and Melchior get the same is one in three.
The probabiliyt that Beltsazar is getting the same pair as Capsar and melchior is also one in three, so we have a combined chance of 4 in 9 that they have the correct set to present.

Well done Pondy

I don't even understand the question this week but I'm sure some of you will.We're back to the 700 thing again! :-
A legion of soldiers consists of several cohorts? of 700 soldiers.
A legion could form a wedge with one soldier on the first rank,two on the second and so forth.
What is the smallest size that a legion could be ?

@venda


If I understand correct, then row three would be three soldiers.
So the question is when is the sum off all integers starting from one divisible by seven.
Reveal Hidden Content

Correct my friend.
I removed the previous post 'cos it showed the hidden content!

A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
What is the smallest number of stripes that it could have
I suspect it's a bit like the map problem where each adjacent country had to be a different colour

@venda said
A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
What is the smallest number of stripes that it could have
I suspect it's a bit like the map problem where each adjacent country had to be a different colour

@bigdogg said
I'm not quite understanding the stipulation. I envision a bunch of horizontal color bars stacked up, but then not every color is adjacent to every other color.

Reveal Hidden Content

@venda said
A flag is made up of 5 colours and consists only of of full width horizontal strips so that each colour is adjacent to each other colour somewhere on the flag.
What is the smallest number of stripes that it could have
I suspect it's a bit like the map problem where each adjacent country had to be a different colour

Reveal Hidden Content

@venda said
No. I didn't understand it either.I think the wording is a bit ambiguous.
I'll post the given answer and explanation hidden
Hidden content removed