Group+5F

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**Please share your strategies for the following problems.** Page 1 - Sudoku: Sebi: Start with the numbers that are on the paper the most like for example 1 appears a lot in the first box so start filling in all the 1's first. Also make a copy of the Sudoku on a scratch paper so that you can erase easily and try more ways!!!

Donny-Write out all of your numbers needed and cross them out when you use them. And double check if it works!  Jacob-Try to use the boxes, lines and columns by filling in the last missing number. Page 2 - Sebi- Imagine this is a tournament and you're watching it. You know that when there are 16 teams there aren't 16 games because each team plays another so you have to always divide by 2 until you get to the final. So start off with 16 and divide by 2= 8 games in the first round. It's easy from then on. 
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Donny-Just divide 16 by 2 and repeat this until the last possible number. Jacob- Consider that half of the teams is competing against the other half. Eight teams remaining and .................  Sebi- Figure out the even multiples of 11 because it says the number is not odd. So those numbers are 22,44, 66 etc... Once you have those 4 numbers figure out which one can be squared and cube. 
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Donny-Start out by listing all of the multiples of eleven and cross them out when they don't work. Jacob- Multiply 2x2=4.......8x8=64 which number to the third power is 64 and which number to the second power 64.  Sebi- The mean is the average. So you add up all the numbers and divide them by the amount of numbers. The mode is the number that appears most frequently and the median is the middle value.
 * 1) 3 Donny-Find the mode, mean and the median.

Sebi- If 20 is the is the value of all numbers added up together and x goes into it, which one of those numbers goes into it? Jacob- Add all the # including X divided by five and make it equal this gives you the answer.Than check it with other 2 options. 
 * 1) 4 Sebi- I don't really get the first one. I've tried it sooooo many times- any suggestions?

Sebi- For the second one i looked at it and saw it was a trapezoid so i tried fitting four trapezoids into it equally. It doesn't matter which way they are facing but at least you will have an equivalent four parted trapezoid. Jacob- Try to use the same shapes as the shape that you have to fill.

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<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Sebi- I measure the board size on the graph paper and then cut it out. I did this so i could play with it and see where it would fit into. <span style="color: #808000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Jacob- 2 pieces of the same shape being smaller on one side and wider on the other side fitting together. <span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">
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 * 1) 2Donny- It may always not going to be the same old pattern.

<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Sebi- At first i thought the nine was after the five but then i saw a patter between the 1, 4, 7 and the 0,3,6. I'll give you a hint: the amount of numbers between 1-4-7 is the same as 0-3-6. Look at those numbers closely and you'll find the pattern quickly.

Sebi- When it says think outside of the box it means that you should not assume the answer right away. This pattern is very obvious once you look at those 6 numbers! :) <span style="color: #808000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Jacob- The pattern changes as you read.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">#3Donny-Take away the decimals for now. Add them later. It makes it easyer. <span style="color: #808000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> Jacob- Calculate the scores in absolute terms (not in %) Sebi- Every next person plays one game less then the person before. So if one person played x games the next person played x-1 games because that next person has already played the other games. The trick is that the first person so A plays the most because he plays everyone and the next person plays everyone but A because he's already played him. <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Donny-Find out how many games just one person would play first. <span style="color: #808000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> Jacob- Think that the first is playing against the other nine, the second player against the remaining eight.............. Page 4 - <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Sebi- Make several of the same boxes on graph paper and then try many different ways to try and put the shapes in. Remember upside-down, sideways- they are all over! <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> Donny-You may also need graph paper for this one too.
 * 1) 4 <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">
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<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Sebi- Look at the shaded part and then look at the diagonal line. How many more isosceles triangles fit into that one half. You take that number and the number shaded and then you have finished half of the fraction. Now all you do is add how many isosceles triangles there are on the other side and then you will have the fraction of the triangle. Sebi- To find the how many square centimeters the whole square is you simply multiply the length times width to find it out. <span style="color: #808000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Jacob- Turn the right shaded triangle to the left and you`ll see that it becomes a square that covers one quarter of the 5x5 square.
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<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Page 5 Cartoon Corner - Hot Ziggety Dog!!
 * 1) 1Donny-Find the lowest commmon multiple for 1-3!!!!!!!!

<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Jacob-Find the lowest common multiple again!!!!!!!!!! Sebi- Use the method of finding the LCM for this one because it really helped me and is a super way of getting the LCM.
 * 1) 2 <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 225%;">Sebi- I made a table (chart) for this one because it helped me with all the numbering. One way to find the lowest common multiple is to make a chart with all the numbers that go into both of them.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">#3 Jacob-Find the lowest common multiple again!!!!!!!!!! <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> Sebi- A way to find the lowest common multiple is to multipy both numbers. But be careful this method doesn't always work.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">#4 Jacob- Multiply the numbers from three with the respective prices.

Sebi- Multipy all the dollors with the products and then you'll find the LCM or lowest common mulitiple. You will also know how much ziggy has to pay for this cookout.