Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)
Ms. Leckman
Games away:
http://www.hellam.net/maths2000/frogs.html
Subscribe to:
Post Comments (Atom)
What's my line?
37 comments:
You start out by moving the first red frog. Then you move the next two yellow frogs. After that you must move the next three red frogs, and then move the next four yellow frogs. The next five red frogs must be moved, then the next 6 yellow frogs, then all 6 red frogs. Move all six yellow frogs again and by now one yellow and one red frog will have reached the other side. Since one frog has reached the other side you have to move five red frogs then five yellow frogs. Then move four red frogs then four yellow frogs. Then three red frogs then three yellow frogs. Then two red frogs and then two yellow frogs. Then move the last red frog and the last yellow frog. You have now gotten all six of each colored frog to the other side. For six red frogs and six yellow frogs the number of moves it takes is 48. The equation to find the total number of moves for any given number of frogs is (f^2)+(f+f) and f is representing the number of frogs.
With the frog puzzle, the easiest way to solve the game is to make the frogs into a red, yellow, red, yellow... or yellow, red, yellow, red... pattern.
Continuously repeat this pattern having each frog jump over another frog of the opposite color. The frogs always have to be in a red, yellow pattern or yellow red pattern (except the frogs you haven't moved at all, and that you are waiting to move).
If you have moved either two reds or yellows so that they end up being right next to each other without the opposite color in between, you cannot solve the puzzle.
If you get the yellow red or red yellow pattern, and can continue the pattern, the puzzle is solved.
Also, the first color you move (for example, red) you would move red once, then you move yellow (the next color) twice, then you move red three times, yellow four times, red five times, yellow six times, and so on until you get all the same color frogs on the opposite side that they were on.
E. Mu. :)
With the frog game, the way that you can solve the game is by moving the frogs in a red then yellow pattern or yellow then red pattern. You continue this pattern by having each frog jump over the opposite color. The frogs always have to be in a red then yellow pattern or yellow then red pattern, or except the unmoved frogs.
If you move two reds or two yellows to where they end up right next to each other without the opposite color in between, you cannot solve the frog puzzle. In the red yellow or yellow red pattern you will solve the problem.
For the first color moved there is one more than that color in the opposite, and it continues like this. An example is that you move one red, you can then have an open spot to move two yellows. Then you can move three reds, and so on until you have six on both sides. A.L. :)
With the frog puzzle, the easiest way to solve the game is to make the frogs into a red, yellow, red, yellow... or yellow, red, yellow, red... pattern.
Continuously repeat this pattern having each frog jump over another frog of the opposite color. The frogs always have to be in a red, yellow pattern or yellow red pattern (except the frogs you haven't moved at all, and that you are waiting to move).
If you have moved either two reds or yellows so that they end up being right next to each other without the opposite color in between, you cannot solve the puzzle.
If you get the yellow red or red yellow pattern, and can continue the pattern, the puzzle is solved.
Also, the first color you move (for example, red) you would move red once, then you move yellow (the next color) twice, then you move red three times, yellow four times, red five times, yellow six times, red six times, yellow six times, red six times, then yellow five times, red four times, yellow three times, red two times, red one time
E. Mu. NEW IMPROVED VERSION
To do the problem you take the red frog once spot starting right to left
Then you move two greens
Then 3 reds
Then 4 greens
Then 5 reds
Then 6 greens
Then 6 reds
Then 5 greens
Then 4 reds
And so on to one of each colors. This will keep a pattern of every other color
K.B
You cannot have 2 of the same color in a row at all while solving this puzzle.
Took me 48 moves
Here’s what I did. I took 7 and moves over to blank then hopped 7 with 6 then move 5 1 space to the right, hop 5 with 7 then hop 6 with 8, move 9 to left once, have 6 hop 9, 5 hop 8, then 4 hop 7, then 3 to the right once, hop 7 over 3, then 8 over 4, then 9 over 5, then 10 over 6, then move 11 to left once, have 6 hop 11, 5 hop 10, 4 hop 9, 3 hop 8,2 hop 7, and 1 move to right, have 7 hop 1, 8 hop 2, 9 hop 3, 10 hop 4, 11 hop 5, 12 hop 6, then u should have a red, yellow, red, yellow pattern. From there you go 6 to right once, then have 5 hop 12, then 4 hop 11, then 3 hop 10, 2 hop 9, 1 hop 8, have 8 go to left once, 9 hop 1, 10 hop 2, 11 hop 3, 12 hop 4, move 4 over once, 3 hop 12, 2 hop 11, 1 hop 10, then move 10 left, 11 hop 1, 12 hop 2, 2 go over to right, then 1 hop 12, then have 12 move right and your finally done!!!
The numbers of moves you should have done should be 48.
KA & IW
You start out by moving the first red frog. Then you move the next two yellow frogs. After that you must move the next three red frogs, and then move the next four yellow frogs. The next five red frogs must be moved, then the next 6 yellow frogs, then all 6 red frogs. Move all six yellow frogs again and by now one yellow and one red frog will have reached the other side. Since one frog has reached the other side you have to move five red frogs then five yellow frogs. Then move four red frogs then four yellow frogs. Then three red frogs then three yellow frogs. Then two red frogs and then two yellow frogs. Then move the last red frog and the last yellow frog. You have now gotten all six of each colored frog to the other side. For six red frogs and six yellow frogs the number of moves it takes is 48. The equation to find the total number of moves for any given number of frogs is (f^2)+(f+f) and f is representing the number of frogs.
E.Ma
To get all of your frogs across the lily pads you must start with either frog in the middle. Then you move the other frog in the middle. Next you would move two frogs of the first color. Then two frogs of the other color, next three frogs, than four etc. make sure you never have more than one frogs of the same color next to each other except the ones you have not moved, or are already on the other side. you do this until you have a pattern of all twelve frogs, yellow, red, yellow, red etc. once you have that you will do the same thing as above except the number of frogs your moving will decrease by one each time.
C.K.
For the P.O.W. this week we had to explain how to get all 12 frogs across 13 lily pads. I found a way that will with 12 frogs and 13 lily pads. First when the website asks you how many frogs you want put in 6 yellow frogs and 6 red frogs. It doesn’t matter what color frog you choose to start with first, but I’m going to use the red frog first. First move the very first red frog, then you want to move two yellow frogs. Then you move three red frogs, four yellow frogs, five red frogs. This is where things get a little tricky you have to move six yellow frogs and six red frogs then four yellow frogs, three red frogs, two yellow frogs and the final frog you should move is one red frog. When you are finished you should end with all 12 frogs on the opposite side that they started on. This technique will work with any number of frogs you choose. If you wanted to do it with different numbers you would have to just change the numbers. For example: If you had a total of 3 yellow frogs and 3 red frogs you would move the first red frog, two yellow frogs, three red frogs, three yellow frogs, three red frogs, two yellow frogs and one red frog. See it works for any number of frogs.
M.G.
I first moved 1 red frog. Then I moved two yellow frogs. Then I moved three red frogs, then four yellow frogs. Then five red frogs, then six yellow frogs,as well as six red as well as yellow frogs. I moved five red frogs, then four yellow frogs.After that I moved the three red frogs then the two yellow frogs then the red frog and I finished. The equation could be F^2 + (f+f) F represents frogs. you plug in the number of frogs of each color.The answer will be the number of moves it takes.
JJ
The P.O.W. for this week asked us to find out how to get 12 frogs across each other to get to the opposite side. The problem gave you 13 lily pads and 12 frogs, (for this I used 6 red and 6 yellow). You can decide what group you would like to move first. In this problem, I will say that I’m going to start with red. The first group moves one then the second group 2. The next 3, then after on the other 4. 5 on your first group, 6 on the 2nd. This is where it gets challenging. You have to do the first group 6 times then the second group 6 again. On the first group 5 the second 4. You keep decreasing the number by 1 each time, until you have won.
That is as hard as our P.O.W. gets this week.
D.M.
in the frog gamer there are 13 lilypads and 12 frogs. 6 on each side(red yellow). so you chose ether side (i picked yellow) and you move the yellow frog once then you move the red frog twice. yellow 3 times, red 4 times. yellow 5 times, red 6 times. yellow 6 times, red 6 times. yellow 5 times, red 4 times. yellow 3 times, red 2 times. then finally, you move the yellow frog one more time and it's done.
K.T.
The pattern for the frogs is:
y=yellow r=red
1(r) 2(y) 3(r) 4(y) 5(r) 6(y) 6(r) 6(y)
and then it is backwards
5(r) 4(y) 3(r) 2(y) 1(r)
and when all these numbers are added together it equal the number of moves. In this case the number of moves was 48.
Proof- 1+2+3+4+5+6+6+6+5+4+2+
=48
So the moves go from one to the max and then the max is repeated two more times. After the max u cound back down to one.
- Another example that this works with all
3v3
1(y) 2(r) 3(y) 3(r) 3(y) 2(r) 1(y)
1+2+3+3+3+2+1
=15
RW
The POW for this weeek wants us to find a pattern on how to move 12 frogs across lily pads.
To get the frogs across the lily pads, you need to make a table. The table will consist of the movses you need to make to move all the frogs across the lily oads.This table will work for any number of frogs because the pattern is you have to move one more than the previous number of frogs. But, after a certain point, start to work backwards, using the same numbers you started with. You will be able to see this pattern in the table. After 6 moves, the table on both sides reverses and the numbers start repeating. Also, at the end of the table, there is an extra number on the red frogs because you have to move one more time to get all the frogs across.
ct
In our POW this week we have solved a problem using colored frogs. We used a total of tweleve forgs, 6 yellow, 6 red. The object was to get the yellow and green frogs from one side to the oppostie side. My partner and I used a total of 48 moves. 24 for each color of frogs. To get them to the opposite side we used a patern. The pattern worked as the following. Move 1 yellow, 2 red, 3 yellow, 4 red, 5 yellow, 6 red, 6 yellow, 6 red, 5 yellow, 4 red, 3 yellow, 2 red, 1 yellow. That gave us our anwser.
KG
A.M.
This was fairly easy and i have broken it down into a couple of easy steps
1. click on one red frog.
2. now, click on two yellow frogs.
3. click on three red frogs.
4. click on four yellow frogs.
5. click on five red frogs.
6. click on six yellow frogs.
7. click on six red frogs.
8. click on six yellow frogs.
9. click on five red frogs.
10. click four yellow frogs.
11. click on three red frogs.
12. click on two yellow frogs.
13. click on one red frog
what you should do is that you are sapose do the game as if it is patten. first you do red then green, green and then red red and then you do green, green, green and then you do red, red, red and then you do green, green and then you do red, red and then you do green, green and then you do red and then you do green and then you are done
You have three yellow frogs, and three red frogs, and you have a blank lily pad.
The trick is to not have two of the same color frogs right next to each other.
First you would move the first red frog.
Then you would move the first yellow frog.
Then you move the SECOND yellow frog.
Then you move the first red frog again.
Then you move the SECOND red frog.
Then move the THIRD red frog.
Then move the first Yellow frog.
Then move the second yellow frog.
Then move the third yellow frog.
Then move the first red frog.
Then move the second red frog.
Then you move third red frog.
Then you move the second yellow frog.
Then you move the first yellow frog.
Then you would move the third red frog.
VB&JS
To get all of the frogs to another side, you can use the equation y = x² + 2x, while x stands for one set of frogs on one side and y stands for total number of moves. However, this only works if there is an even number of frogs on each side. To find the number of moves it will take to move an odd number of frogs, you must use the equation y = x² + 2x - .25, and you must plug in the range of the two sets of frogs. This will give you a decimal, and when plugged in for x, you will end up with an extra .25, so you must subtract to get a whole number move quantity. Below is a table of our data.
1 frog - 2 moves
1 by 1 frog - 3 moves
1 by 2 frogs - 5 moves
2 by 2 frogs - 8 moves
2 by 3 frogs - 11 moves
3 by 3 frogs - 15 moves
3 by 4 frogs - 19 moves
4 by 4 frogs - 24 moves
4 by 5 frogs - 29 moves
5 by 5 frogs - 35 moves
5 by 6 frogs - 41 moves
6 by 6 frogs - 48 moves
C.Vdv.
DUCT TAPE RULES!!!!!!!!!!!!!!
For the P.O.W this week we had to explain how to get all 12 frogs across 13 lily pads. I found a way that will work with a total number of 12 frogs and 13 lily pads. First when the website asks you how many frogs you want to put, you want 6 red frogs and 6 yellow frogs. It doesn’t matter what color frog you choose to start with first, but I’m going to use the red frog first. First move the very first red frog, then you want to move two yellow frogs. Then you move three red frogs, four yellow frogs, five red frogs. This is where things get a little tricky. You have to move six yellow frogs, and six red frogs. You do one more six yellow frogs. Then five red frogs, four yellow frogs, three red frogs, two yellow frogs, and one red frog. When you are finished you should end with all 12 frogs on the opposite side of where they started on. If you wanted to do it with different numbers you would have to just change the numbers. For example: If you had 3 yellow frogs and 3 red frogs you would move the first red frog, two yellow frogs, three red frogs, three yellow frogs, three red frogs, two yellow frogs and one red frog. See it works for any number of frogs.
M.G.
This week for the P.O.W. we had to move 12 frogs across 13 lily pads. You do this by moving one red frog on to the middle lily pad then you take the green frog ond move that on to the open lily pad then move the red frog on to the open lily pad. You repeat this over and over again. The trick to this is you never have the same color frog in a row.
J.B.
the pattern is x squared+2x
for example, for 6 frogs, it takes 48 moves.
6x6=36
6x2=12
36+12=48
this equation works for any number.
A.H.
To get all the frogs across the lily pads there is a pattern you must follow. You start by moveing the frog in front on the red side then two on the yellow and so on intill all six have moved, then it's the same thing but six each time. Make sure when moveing the frogs that at the end of each row is a frog to jump over of the other color or you will block.
E.K.
POW
By, CH, NH
Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)
1. Click in this order:
2. First red frog,
3. First green frog,
4. Second green frog,
5. First red frog,
6. Second red frog,
7. Third red frog,
8. First, Second, Third and Fourth green frogs in that order,
9. First-Fifth red frogs in order,
10. First-sixth green frogs in order,
11. First-sixth red frogs in order,
12. First-sixth green frogs in order,
13. Second-sixth red frogs in order,
14. Third-sixth green frogs in order,
15. fourth-sixth red frogs in order,
16. fifth-sixth green frogs in order,
17. Then last, sixth red frog.
Congratulations you win!
First of all, you should never have two of the same color frogs together that you already moved. I will refer to the first, second, third, fourth, etc frogs. The first frog is whichever, whenever frog is towards the middle the most for each color. If two same colored frogs are the same number of spots from the middle I will say the left or right frog. First move the first green frog. Move the first red frog. Move the second red frog. Move the first green frog. Move the first left green frog. Move the second left green frog excluding the middle frog. Move the third left green frog. Move the first left red frog. Move the first red frog. Move the second right red frog. Move the fourth right red frog. Move the first right green frog. Move the middle green frog. Move the first left green frog. Move the second left green frog. Move the fourth left green frog. Then starting with the nearest red to the green frog you just moved, move every red frog going right. Then move every green frog you can going left. Keep doing these last two steps and you will solve the puzzle.
J.K. the Blondie
I got all 12 frogs over to the other lily pads in 48 moves. Its goes like this (every simi- collon means a diffrent color
1;1,2;1,2,3;1,2,3,4;1,2,3,4,5;1,2,3,4,5,6;1,2,3,4,5,6;1,2,3,4,5,6;1,2,3,4,5;1,2,3,4;1,2,3;1,2;1.
Question: Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)
R.B.
J.B. P.o.w.
To beat the frog puzzle first you have to click on one frog from each side and then after that you click on another frog from any side lets say this is the green side so after you click on a green one then you click on two from the red side. Then your pattern continues as you continue green will always be ahead by one. Until all frogs are on each side with the rest of their colors.
Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-) Problem of the week MRG/SASp8/9
It took us 48 moves to get the frogs from one side to the other. It ends up at 48 because x squared plus 2x, so the number of once color of frog, lets say six time six is thirty-six plus 2x (this time six) is twelve plus thirty-six is 48. That is the amount of moves it takes to do it with forty-eight. Here is the table of frogs that explains each amount of frogs and how the equation.
# of frogs of each color Equation Answer
1 1x1+2x1 1+2=3
2 2x2+2x1 4+4=8
3 3x3+2x3 9+6=15
4 4x4+2x4 16+8=24
5 5x5+2x5 25+10=35
6 6x6+2x6 36+12=48
Red dots= red frogs
Dark green circle=Lily pad
Lime green dots= yellow frogs
In the Game we had to be able to get all of the frogs to the opposite sides, and then find out how many moves it took.
It took 48 moves to get all of the frogs to the opposite sides.
In order to do this there always had to be a Yellow frog in front of the red and a red frog in front of the green one. The pattern went like yellow, red, yellow, red. You never wanted there to be two of the same color frogs next to each other while you were moving them and you never wanted a space in between them. There should only be a space on one end.
At 10 moves your game would look like this.
-HR
D.E.
POW for the Week of September 17th
Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)
This is the list of moves to make all the red and yellow frogs go on their opposite sides. First, click the first red frog, the first green frog, third red frog, fourth green frog, fifth red frog, sixth green frog, sixth red frog, sixth green frog, fifth red frog, fourth green frog, third red frog, second green frog, and fist red frog, those clicks should add up all 48 moves which takes to solve the puzzle. This will work as long as you add one to each side, leave an empty space, and don’t have to frogs stick together besides there starting and beginning positions. It’s a hard logic puzzle, which requires a lot of thinking to it.
The problem in POW is you have to find a way to get the yellow and pink frogs to the other side of the lily pads. This means that you have to find a way to get all the frogs to the other side without making them get stuck.
I first started out trying out the problem a couple of times, and would always have to restart it. Then, I saw that there had to be a pattern in the way that I moved the frogs to the other side, and if I moved the frogs to where there was a one frog that was the same color facing another frog the same color, than I would have to restart.
I figured out how to do it, and you always have to have a pattern of yellow, pink, yellow, pink at all times, or you would never be able to get them to the opposite side.
This is assuming you have 6 frogs on each side. First of all, you should never have two of the same color frogs together that you already moved. I will refer to the first, second, third, fourth, etc frogs. The first frog is whichever, whenever frog is towards the middle the most for each color. If two same colored frogs are the same number of spots from the middle I will say the left or right frog. First move the first green frog. Move the first red frog. Move the second red frog. Move the first green frog. Move the first left green frog. Move the second left green frog excluding the middle frog. Move the third left green frog. Move the first left red frog. Move the first red frog. Move the second right red frog. Move the fourth right red frog. Move the first right green frog. Move the middle green frog. Move the first left green frog. Move the second left green frog. Move the fourth left green frog. Then starting with the nearest red to the green frog you just moved, move every red frog going right. Then move every green frog you can going left. Keep doing these last two steps and you will solve the puzzle.
J.K. the Blondie Boy
The problem in POW is you have to find a way to get the yellow and pink frogs to the other side of the lily pads. This means that you have to find a way to get all the frogs to the other side without making them get stuck.
I first started out trying out the problem a couple of times, and would always have to restart it. Then, I saw that there had to be a pattern in the way that I moved the frogs to the other side, and if I moved the frogs to where there was a one frog that was the same color facing another frog the same color, than I would have to restart.
I figured out how to do it, and you always have to have a pattern of yellow, pink, yellow, pink at all times, or you would never be able to get them to the opposite side.
JW
In the POW, every pink frog has to have a green in front of it and every green frog has to have a pink in front of it. I made sure that there was a pattern all the time. It took me 48 times
EK
O. S.
9/21/07
P. O. W.
Question: Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)
Solution: I got all 12 frogs over to the other side in 48 moves. I saw a pattern in moving them to the other side. The pattern increases by moving one frog every step until you get to six, then it goes by six three times and then decreases by one frog each step. It goes like this:
1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,1,2,3,4,1,2,3,1,2,1
POW 9/21/07
I figured out the lily pad game by experimenting moving frogs until I found a pattern. You move all the frogs in the pattern for 48 moves and then you have the solution!
SV
C.H.C. period 8,9 Mrs.L
When there is six yellow and six red frogs make the frogs in a pattern of yellow red yellow red or red yellow red yellow which is the rule for the frogs until they’re on the other side. You can make this pattern by moving the first red frog one petal and then the yellow frog jumps the first red frog. Next move the yellow frog next to the first red frog then after start making the pattern of red yellow red yellow once that’s done move all the frogs to the other side to win this also could be done the opposite way.
Order: 1 1,2 1,2,3 1,2,3,4 1,2,3,4,5 1,2,3,4,5,6 1,2,3,4,5,6 1,2,3,4,5,6 1,2,3,4,5 1,2,3,4 1,2,3 1,2 1
Post a Comment