![]() ![]() We now know that $k_4 = 6$, it may be an interesting starting point to see if anyone can find a solution for $n=5$ using $7$ lines, as we know that $6$ is impossible and $8$ is possible. Wiki User 22:01:28 This answer is: Study guides Word Games 20 cards What word means 'hurry'. ![]() ![]() Let m n/2 // For each line we draw, we divide points // into two sets such that one set is going // to be connected with i lines. Best Answer Copy A line from 1 to 2, a line from 2 to 3, and a line from 3 to 4. Below is recurrence relation for the same. Each set needs to be connected within itself. Watch popular content from the following creators: AK(eyykeyy), Math tricks(mathtricks89), 99GOONSQUAD. When we draw a line, we divide the points in two sets that need to connected. Discover short videos related to 4 dots connect on TikTok. I think it is impossible to actually connect $n -1$ dots with every line (except the first), which improves our lower bound: We need to draw n/2 lines to connect n points. Now because $n^2 - n = n \cdot (n-1)$ this means that we must atleast need $n$ lines for the $n^2 - n$ dots that remain after the first line. Discover short videos related to 4 dots connect with 3 lines on TikTok. My question is: Can we improve the lower or upper limit? Does there even exist an $n\geq 4$ such that $k_n < 2 \cdot (n-1)$?ĮDIT: After some thinking, I think we can assume that only the first line can connect $n$ dots, and all the following can at the most connect $n-1$ dots. Therefore we can conclude for $n \geq 4$ that: This gives us $k_4 \leq 6$ (using what I found out in the edit, this becomes $k_4 = 6$) and in general $k_n \leq 4 + (n-3)\cdot 2 = 2\cdot (n - 1) $ as we need two more lines for every step larger then $3$.įurthermore, we know that $k_n > n$ because every single line can connect at most $n$ points, and we need to connect $n^2$ points, and we must have double points. It is impossible to connect all the dots using only three lines, which gives us the minimal number of lines for $n = 3$ with $k_3 = 4$.įor $n = 2$, we easily see that $k_2 = 3$:įor $n \geq 4$ we can use the trick we used for $n = 3$ and then just expand from there: DIRECTIONS: Connect the dots by drawing a line that matches column A with the correct answer on column B. What is being represented by the lines connecting the dots 4. My question is, what is the minimal number of lines (let us call this number $k_n$) for an $n\times n$ grid to connect al the dots using only straight consecutive lines connect the number to a dots by connecting line that match the picture with it's correct description 3. The solution is to think outside of the box and do the following: Whereas center-aligned text is often used for shorter lines of text. Draw a $3 \times 3$ grid, and connect all the dots using only $4$ straight consecutive lines. To open the type settings panel, click the three dots in the bottom-right corner of. ![]()
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