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EXCEL is wonderful! I have used my equation H=3n2+3n+1 to calculate all the hexagons in the NESTED HEXAGONS and then this algorithm to identify the PRIME NUMBERS found in the H columns:

=IF(B9=2,"Prime",IF(AND(MOD(B9,ROW(INDIRECT("2:"&ROUNDUP(SQRT(B9),0))))<>0),"Prime","Not Prime"))

Place e.g. the algorithm in a cell opposite B9 and write in B9 and then CRL + SHIFT + ENTER in the address box to activate it.

Scroll down to include all the H cells and the list will read off the PRIME cells.

See: http://www.excelexchange.com/prime_number_test.html

I have competed 1000 NESTED HEXAGONS in pretty quick time with 3,003,001 elemental hexagons. The algorithm works up to 268,435,455 – I am NOT going to the limit!!

The PRIME NUMBER (P) hit ratio is steady diminishing and has reached ~1/4, having generated 254 P’s for 1000 NESTED HEXAGONS.

This exercise was fun but of what use?

]]>What is your favorite color? Name something that suits your color.

Choose from:

Red

Orange

Yellow

Green

Blue

Indigo

Violet

Why the options are rainbow color only? Where are black, white, grey, pink, brown, and purple (slightly different than violet)?

]]>Step 3 should be replaced by the following steps:

Step3a: Shore ABCDbcd, Island -, Over a

Step3b: Shore ABCDd, Island bc, Over a

Square root of 2, 3, 5, so on...

How about √p, for p prime?

]]>Cheers, math9maniac.

]]>Welcome to the forum. Thanks for your comment.

I've just tried this puzzle.

I understand your point. I think you're meant to assume that each (male) friend takes his two marbles, looks at his label and makes his deduction in isolation. Only Sally has access to all three statements. Maybe it's because women are better listeners.

Here's my reasoning:

There are four possible set ups and four possible labels: BBB, BBY, BYY, YYY.

If someone looks at their label and is able to say what the hidden colour is, their label must have two colours in common with what they picked.

eg. For Tom, he knows he has BBx. If the label is BYY or YYY, then he cannot say what his third colour is because there are two possibilities. But if his label says BBY then he knows he has BBB, and if his label says BBB, then he knows he has BBY.

So from his statement we can deduce Tom's label is either BBB or BBY.

From Richard we can deduce his label is either BBY or BYY.

Harry does not know his third colour so he isn't looking at a label that is either BYY or YYY, so he must be looking at a label saying BBB or BBY.

Thus, between them Tom and Harry have the BBB and BBY labels. This means that Richard must have the label BYY.

As he can deduce his third colour, he must have BBY. So Tom must have BBB.

Sally can deduce her label is YYY just from the other three labels.

So she doesn't have YYY. Therefore Harry must have YYY.

So, finally, Sally has BYY.

Note to MIF. This puzzle could be worded to cover this point.

eg.

Years ago, to puzzle his friends, a scientist gave one of four containers containing blue and/or yellow marbles to each of the friends; Tom, Richard, Harry, and Sally.

There were 3 marbles in each container, and the number of blue marbles was different in each one. There was a piece of paper in each container telling which color marbles were in that container, but the papers had been mixed up and were ALL in the wrong containers.

He then told all of his friends to take 2 marbles out of their container, read the label, and then tell him the color of the third marble.

Harry went first. He took 2 yellow marbles from his container. He looked at the label in his container, but could not tell what color the remaining marble was.

Then Tom took two blue marbles out of his container and looked at the label. He was able to tell the color of the third marble immediately.

Then Richard took 1 blue marble and 1 yellow marble from his container. After looking at his label he was able to tell the color of his remaining marble.

Sally, without even looking at her marbles or her label, was able to tell the scientist what color her marbles were. Can you tell what color marbles Sally had? Can you also tell what color marbles the others had, and what label was in each of their containers?

Bob

]]>so this is how site's answer goes:

Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie....

Working backwards:

2 Pirates: Duncan splits the coins 0: 100 (giving all to Eddie). Otherwise, and perhaps even then, Eddie would vote against him and over he goes!

3 Pirates: Colin splits the coins 99 : 1 : 0. Eddie is going to vote against him no matter what (see above) so gets nothing, but Duncan will vote for him, to get at least one gold out of it (if Duncan votes against him, there will only be two pirates remaining and Duncan will get nothing, and may even lose his life!)

Okeh.. here comes the diversion to the perspectives.. 1st perspective is what is given In the original solution, and the answer turns out to be 97:0:1:0:2

Okeh, now for 2nd perspective.. see.. in the original answer in 4th stage when billy turned in he devided the money as 97:0:2:1

And duncan and eddie accepted the deal assuming that they will get more than before.. yeah definitely eddie gets more than before, but duncan's decision is ambigous! Because billy and collin both are trying to please duncan consequtively, to get his vote(where as in eddie's case only billy is trying to please him!)

since billy and collin both are tryin to please him, it wouldnt be right to assume that in future if billy dies and 3rd stage arrives then collin will give him only 1 pence.. because of the ambiguity i explained above! it was possible in 3rd case maybe collin was thinking of giving 3 pence! After all collin and duncan are not instant enemies(as against duncan and eddie)..

Duncan can in no way quantitatively judge who will give him more pence, collin or billy? And since Duncan is a blood thirsty naughty(like other pirates) he will most probably try to kill the most number as possible, so it is equally likely that duncan will vote against billy! Now we already know what happens if duncan votes for billy(as given in site's answer) so lets speculate what would happen if duncan votes against billy, it would mean billy has the possibility to die!

So now, when 5th stage arrives:

5 pirates: alex devides the coins as 98:1:0:0:1

billy will vote (because its 2nd perspective and i already explained it)

eddie will also vote because if alex dies, billy dies and in collin's case he gets a 0!!

See... so 2 possible aswers were possible all because duncan's decision got an ambiguity.. we cant say giving duncan a 2 pence by billy will satisfy him.. since collin also is trying to please duncan and also he is not his instant enemy(in ver. 1 [also in logics section]collin was duncan's instant enemy... billy was collin's instant enemy and all..)

so logically there is no.guarrantee that duncan will vote for billy.....

at the same time duncan can vote for billy assuming he gets more pence, but think if actually such a situation comes forth wont collin and billy bargain increasing each penny? (Eg. Collin can say duncan to vote against billy instead he(collin) will give more than 2 penny.. like an oath or promise among pirates? It wasnt really necessary that in 3rd case collin would give him only 2 pence!)

yeah i can gurantee 1 thing... if the pirates are not business minded then yeah site's answer will come out to be correct... but that would just mean those pirates are not intelligent! and yet they are quite intelligent... think about it... these are the 2 perspectives i meant!

That question would have been better if ver. 2 was not made!

i just started this thread to explain something with relevance to my previous thread "5 pirates puzzle ver.2"

i wanted to explain what i meant by "instant enemies"

see.. in that puzzle if a pirate feels 'its better for me if this person did not exist' then that 'this person' is his instant enemy, that is what i meant.. eg. In ver. 1 collin was duncan's instant enemy and billy was collin's since in billy's absense collin got 99 pence but in presence he gets 0 pence.. similarly in collin's absense duncan got 99 pence but in presence only 0.. the difference in their gains is extremely high!

but in ver.2 thats not true.. in billy's presence and absence the difference of money duncan gets is only 1 pence.. so billy or collin neithet of them is duncan's instant enemy.. and since 2 consequtively old pirates came into scene who are not duncan's instant enemies.. that is wha makes duncan's decision ambigous!