There exist an infinite plane with infinite number of dots. For sake of argument, let's assume they are 1 inch away from each other.
However, below(on your far left) you can see 3 lines already made. The last line is the yellow one.
What you see on the right, are all combinations of possible moves. Move is defined as structure of lines until you reach an empty dot.
Thus, there are 6 combinations of single line(on top). While on bottom you see 10 combinations. 5 of them moves with 2 lines, and 5 with 3 lines.
Total # of combinations is 16.
So far so good?
Well the basic unsolved question are:
* Does formula exist to calculate total number of combinations(16 in this case) just by looking at the initial graph of 3 lines?
** Does formula exist to show the breakdown of all combinations (6 for single line, 5 for 2 lines, 5 for 3 lines?
*** is 16 the biggest number of combinations that you can make from 3 line starting configuration? For instance: Try to calculate # of combinations (1 lines, 2 lines, 3 lines) from this initial variation:
To not spoil the fun, i will just say there is more than 16. So is this the best solution? How we can prove that this is the best we can do? Obviously we can prove that just by doing all 3 line configurations by hand, but what if we take it to next level? What's the best 4 line configuration and how many combinations it has? How about 5,6.7...(n) ? The tree expands quite rapidly, and also few things need to be explained:
Combinations vs Permutations:
Above, there are 4 lines as starting configuration. In this case, there are 36 combinations OR 41 permutations. The reason is because you can go from A > B > C > D or C > B > A > D. Once again, is there a formula to calculate combinations (36) and Permutation(41) from any starting configuration?
Notation + Final info to consider:
Using above notation, you can notice that each configuration is unique and might have different #s of combinations and or permutations. For example:
Anyone with any input, either mechanical or potentially writing a code to get the answers How many combinations/Permutations for each variation with up to 10 lines as a starting configuration, would be greatly appreciated. If your program can handle bigger starting configurations, that's even better!
Thank You and enjoy!
I read this from a book and it looks a bit like a the classical "rope burning question". However, in the classical question (eg. https://tzookb.com/two-ropes-brainteaser), you are given two ropes where each rope takes an hour to burn from one end.
In the book I read, however, you only have ONE rope, so I couldn't figure out how to time 15 minutes. Could anyone figure out a way to time 15 minutes with just one rope? Could there be a mistake in the book?
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1a) Always start in the square to right of center square
!) you are always traveling diagonally down to the right; when you exit the right side,you move down one row then jump left to farthermost open square
2) moving diagonally down to the right.you will exit the bottom..move one column right and jump
up to the highest open square
3)When you are trying to move down and right and you encounter a numbered square
...you go in the upper left corner and out the upper right corner ending on the same row
you started
3 a) If the above move puts you out side the main grid then you jump back to the left as far as poss on that row
3 b) If you are still inside the big grid,then you move down to the right as before
3 c) when you exit on the main diagonal Move to the left as far as possible in the bottom row
4) The above are all repetitive moves and allow you fill in any odd numbered grid such that all columns ,all rows and the diagonals add up to the same sum
I once read over the internet a question like:
You have a knife which is very sharp and a rope of unifoirm length, with a single cut what is the probability that the rope is cut exactly from half.
The who gave the answer 1/3 had the logic that there are only three possibilities of this experiment after the cut.
1. Left peice is bigger
2. right peice is bigger
3. left peice = right peice
so the probability he calculated is 1/3.
When i discussed with some of my friends they were not convinced on this answer, arguing that this type of experiment can have infinite possibilities.
Can someone please help and explain the correct answer if it exist at all.
Regards
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A friend asked me this one: What is the minimum distance from the Earth to Mars, in kilometres?
He also showed me this: 1.8668509 x 10^{-6} pc
After searching a bit I've learned that the minimum distance from the Earth to Mars is about 54.6 million kilometres, but my friend says that the answer is not correct and that I have to look to the "formula?" he showed.
I ask you to give me a hand on this one, because I'm stuck...
Thank you!
]]>I've created a puzzle based game at PuzzlePost.uk that can be sent as a gift in the post - it might be useful for those who haven't been able to see friends and family for a while.
It contains a range of puzzles to test various different aspects of your thinking.
I hope you like it.
Thanks,
Will
]]>There is a troupe of five mummers: a drummer, a dancing bear, a piper, a juggler, and a jester. One always tells the truth, one always tells lies, and the remaining three tell a mixture of truth and lies. To find out who tells what, the following clues are presented:
Drummer: I always tell a mixture of truth and lies.
Juggler: That is not true.
Jester: If the bear is always truthful, the juggler tells nothing but lies.
Bear: That is false.
Piper: The drummer always tells the truth.
Jester: The piper tells nothing but lies.
Can you figure out who tells what based on this information, and how?
]]>There are two which I still can't solve after driving myself nuts looking at them.
Perhaps this is a good place to get the problem solved?
The questions all involve a 3x3 matrix and there is usually a logic sequence going from left to right, and sometimes also up to down. The idea is to supply the missing corner chosen from the eight samples below.
]]>George got a birthday present which was 1 banknote of 100 (the currency does not matter. Lets name it "currency" just for convinience). Valid banknotes in the currency are: 100, 50, 20, 10, 5, 2 and 1.
So he decided to spent some of the money in the shopping mall (he did not take any other banknotes with him. Just the one banknote of 100). At the end of the shopping it turns out that:
1. In each and every shop he bought just one item and therefore just one payment was made.
2. The price of the item was a whole integer (no decimal points are allowed)
3. For each item he never had the exact sum that's why he always gives the nearest banknote (of which he had at the moment).
4. The sellers on the other hand always have enough money in different banknotes that's why they return the change with as less banknotes as possible. However, at the end it turns out that each seller aways return at least two banknotes to George.
The question is:
What is the maximum number of items that George can buy with these restrictions?
I have bolded the important parts in my opinion, so they pop out.
The approach that I took was the following:
1. In each shop the way I tried to figure out the price of the item is to have a change with as less as possible banknotes as change and with as much as higher value of the banknotes in the change
2. And as less as the price can be.
So the solution:
1. First Shop one buying of item that costs - 10
- The payment was made with the available banknote - 100
- The change was - 50 20 20
- Available banknotes for George - 50 20 20 = 90
2. Second Shop one buying of item that costs - 9
- The payment was made with the available banknote - 20
- The change was - 10 1
- Available banknotes for George - 50 20 10 1 = 81
3. Third Shop one buying of item that costs - 7
- The payment was made with the available banknote - 10
- The change was - 2 1
- Available banknotes for George - 50 20 2 1 1 = 74
4. Fourth Shop one buying of item that costs - 9
- The payment was made with the available banknote - 20
- The change was - 10 1
- Available banknotes for George - 50 10 2 1 1 1 = 65
5. Fifth Shop one buying of item that costs - 7
- The payment was made with the available banknote - 10
- The change was - 2 1
- Available banknotes for George - 50 2 2 1 1 1 1 = 58
6. Sixth Shop one buying of item that costs - 9
- The payment was made with the available banknote - 50
- The change was - 20 20 1
- Available banknotes for George - 20 20 2 2 1 1 1 1 1 = 49
7. Seventh Shop one buying of item that costs - 13
- The payment was made with the available banknote - 20
- The change was - 5 2
- Available banknotes for George - 20 5 2 2 2 1 1 1 1 1 = 36
8. Eight Shop one buying of item that costs - 17
- The payment was made with the available banknote - 20
- The change was - 2 1
- Available banknotes for George - 5 2 2 2 2 1 1 1 1 1 1 = 19
I tried different approaches and this gives me the highest number of items - 8. For the last three we have several options but they cannot give more than 8.
Is this the correct answer and if no how can you approach the problem to have more buyings. I found the rule that sellers should return at least two banknotes the most restrictive.
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Original: http://brainden.com/forum/topic/11943--/
My Additions: http://brainden.com/forum/topic/12010--/
]]>This is an easy one... how many can get it first time?
]]>this is actually an old problem solved by vos Savant, and I can't get to the bottom of it. It goes like this:
A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?
Savant replied "one out of three".
I convinced myself pretty hard that the answer should be 2/3, so I'm looking for explanation of Savant's answer.
If at least one is a male, and you have 2 puppies, one yellow and one green collar, there are 3 possible combinations (I agree with her so far):
YM & GM
YM & GF
YF & GM
So, if you choose Y collar, there is 2/3 chances, that the other one is a male, and of course the same for G collar.
Where did I get it wrong?
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In order to determine which of the 10201 cases is defective, the manufacturer has two scales at his disposal:
How can the manufacturer determine the defective case using only 2 times each of the 2 scales?
Second version of the riddle
A poker manufacturer has created 41010 cases each containing 100 chips.
41009 of these cases are perfect and each of their chips weighs 10g.
One of these cases is defective and its 100 chips weigh 11g each.
In order to determine which of the 41010 cases is defective, the manufacturer has two scales at his disposal:
How can the manufacturer determine the defective case using only 2 times each of the 2 scales?
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Market segmenting is the process of dividing the market into groups who have distinct needs, wants, behaviour or who might want different products and services. Segmentation is usually done along demographic, geographic, attitudinal or behavioural lines. Small segments are often termed niche or speciality markets. However, all segments fall into either consumer or industrial markets.
Assuming the assertion in the above argument are true, which statement must be true?
A. Niche markets are primarily in the consumer space.
B. Segmentation starts with easier demarcations such as geographical and demographical boundaries, and over time, can move into finer directions, such a attitudes and behaviours.
c. The value of market segmentation is that it allows companies to hone and target their marketing messages to different groups , depending on where they live, what their attitudes are,and what behaviour they display.
d. A niche market maybe composed of a group of individuals that share specific characteristics across different segmentation lines , such as living in the same areas, being of a certain age, having similar attitudes, and engaging in similar behaviours.
e. Industrial markets tend to fall more along geographic lines and consumer markets more along demographic, attitudinal, and behavioural lines.
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She said I was a genius. But I said there were two ways to arrive at the answer, and I simply chose the easier way.
A 6-inch [long] hole is drilled through [the center of] a sphere.
What is the volume of the remaining portion of the sphere?
The hard way involves calculus. The easy way uses logic.
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