04 Dec '21 10:11

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**- Joined
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S.Yorks.England- Joined
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Wherever@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- Joined
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S.Yorks.England@bigdogg

Excellent big dogg.*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

Correct- Joined
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S.Yorks.EnglandMust 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**- Joined
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Linkenheim@venda

It's that season ðŸ˜‰

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.- Joined
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S.Yorks.England- Joined
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S.Yorks.EnglandI 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**?- Joined
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Linkenheim@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 ContentAfter 175 rows we have have 15400 soldiers. They are organized in 22 Cohorts.

in fact I wrote a little formula into Excel to find the numbers.- Joined
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S.Yorks.England- Joined
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S.Yorks.England- Joined
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S.Yorks.EnglandA 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- Joined
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Wherever@venda

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.*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- Joined
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S.Yorks.England@bigdogg

No. I didn't understand it either.I think the wording is a bit ambiguous.*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.

I'll post the given answer and explanation hidden

Reveal Hidden Content11. On an n stripe flag there are n-1 places where two stripes meet so at least 11 stripes are needed.Using digits to represent colours 12345314251 is an example solution- Joined
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Linkenheim@venda

So I understand we need to design a flag made up of horizonatl stripes,in which we ensure that each colour has at least one neighbour with each colour.*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 ContentEvidently we need to have each colour more than once. If I replace the colour by number my first design is 12345.

I add a 2 between 4 and 5 and get 123425. Now for 2 the condition is set. I can add a 1 between 3 and 4: 1231425 (I keep in mind that I want to make another 1 to neighbour to 5.

If I add a 4 at the end and a 3 I get

123142543 and have now 2 and 4 statisfied.

with the addition of 5 and then1 I get

12314254351

That is eleven stripes. It is a solution, but maybe not the optimum. I can't get my head around for a formula, so I did it by hand ðŸ˜‰- Joined
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Linkenheim@venda

Seems that I got the wording right.*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**