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Interesting Question

In the Samsung Galaxy Tab, you can put a passcode to protect it. There are 9 dots on the passcode. You have to connect at least 4 dots to make a combination password. How many passcodes can you make? Details: 1. If you try to connect one corner to another corner, it counts as THREE dots. This is because there is a dot in between. 2. Order DOES matter. 3. Have fun! This is a problem I have thought about for a few days, but have no idea where to start.

Note by Anton Than Trong
3 years, 8 months ago

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This is a great example of interesting questions which students submit that get rejected because they aren't clearly phrased. You have an opinion of what can be done, but that has not been conveyed well which results in some confusion.

For example, you have not provided the basic explanation of what can, or cannot be connected. For example, can I connect up \(1-3-2-5\)? I believe that your answer is no, but I do not see which aspect this will contradict.
Can dots be reconnected again - i.e. is \(1-2-3-2\) valid?
What does Condition 1 really mean? It is badly phrased, and I can think of several different interpretations of it.

As always, it is important to express yourself clearly, so that you can easily be understood by others, who would then be able to give you better feedback about how to approach the problem. Calvin Lin Staff · 3 years, 8 months ago

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@Calvin Lin master Calvin please help over this topic.... Riya Gupta · 3 years, 8 months ago

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I understand what he's trying to say: The 9 dots are arranged in a 3x3 grid. A passcode is formed by joining at least 4 of these dots with lines. You can NOT choose a dot more than one time, however it is possible to draw a line passing over an already selected dot, but then it won't be registered again. Condition 1 means that you can't draw a line over a dot without selecting it. So if you draw a line from e.g. the bottom left corner to the upper left corner (and the dot in between is not already selected), you will select the point in between them as well. Any questions? Mattias Olla · 3 years, 8 months ago

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@Mattias Olla The problem implicitly relies on the assumption that one understands the workings of the passcode on the Galaxy Tab. The issue is that you are reading more into the question than is currently stated.

Additional constraints that you added were
1. You cannot choose a dot more than one time.
2. The path is formed using straight lines. This implies that we can't connect 1 to 9 without also choosing 5. 3. It is possible to draw a line over a chosen dot.

Is this set of additional constraints a necessary and sufficient set? Are there any other conditions that are missing? Any other edge cases that we need to consider? Calvin Lin Staff · 3 years, 8 months ago

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@Calvin Lin This is the list of full and complete restraints of the problem. Bob Krueger · 3 years, 8 months ago

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@Calvin Lin Yes, that's what I realized too. The start and end dots can be chosen however you like. Apart from that, I believe that's sufficient. Mattias Olla · 3 years, 8 months ago

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Akshat J, could you please explain your answer? Anton Than Trong · 3 years, 8 months ago

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4 dots: 1624 solutions Suryansh Shrivastava · 3 years, 8 months ago

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its not a straightforward permutations question, the answer changes based on the choices you make for the 1st, 2nd and 3rd dot. Suryansh Shrivastava · 3 years, 8 months ago

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@Suryansh Shrivastava but its written atleast 4 dots means more can be possible Riya Gupta · 3 years, 8 months ago

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by the way when you join two corners there are 3 dots involved, so why does it count as two? Aditya Parson · 3 years, 8 months ago

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@Aditya Parson It connects the corner spots directly, passing over the middle one. Got? Muhammad Abdullah · 3 years, 8 months ago

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@Muhammad Abdullah Yeah but 3 dots are involveD? Aditya Parson · 3 years, 8 months ago

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16 Kuldeep Ugale Patil · 2 years, 11 months ago

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9C4 ways .There are 9 dots,while each combination takes up at least 4 dots. Harsa Mitra · 3 years, 8 months ago

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@Harsa Mitra No, it is not that straight forward. There are restrictions on how the patterns are formed. Mattias Olla · 3 years, 8 months ago

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Thank you for the correction. Anton Than Trong · 3 years, 8 months ago

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@Anton Than Trong No problem. Aditya Parson · 3 years, 8 months ago

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362844 Akshat Jain · 3 years, 8 months ago

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@Akshat Jain HOW? Muhammad Abdullah · 3 years, 8 months ago

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@Akshat Jain did u took the cases of selecting 4 and more dots out of 9 and adding them? Riya Gupta · 3 years, 8 months ago

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@Riya Gupta and permuting would exceed his answer. Aditya Parson · 3 years, 8 months ago

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@Riya Gupta That would never yield that many results. Aditya Parson · 3 years, 8 months ago

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@Aditya Parson may be possible......but sooo big digit answer.......??????!@ Riya Gupta · 3 years, 8 months ago

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@Riya Gupta I already tried that logic it would reach around 700,000. Aditya Parson · 3 years, 8 months ago

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@Aditya Parson ok.....but how to begin with this question? Riya Gupta · 3 years, 8 months ago

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@Akshat Jain uhmm..how? Aditya Parson · 3 years, 8 months ago

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