The green frogs are going to change places with the brown frogs, but must observe the following rules.
• A frog can hop to an adjacent pad. • A frog can jump over another frog to an unused pad.
• A frog cannot move backward. For example, once a frog moves to the right, it can only continue to move to the right.
1. What is the minimum number of moves needed to have the green frogs switch places with the brown frogs? Describe the movement of the frogs.
http://www.mofunzone.com/online_games/frog_leap.shtml#
SOLUTION:
The minimum hops is 15. I have included a visual for you. You could have drawn the problem out or created a table to help you solve the problem.
14 comments:
ZB
1. The minimum number of moves it will take to move each frog is 16. I got this by making this:
G G G o B B B
G G o G B B B
G G B G o B B
G G B G B o B
G G B o B G B
G o B G B G B
o G B G B G B
B G o G B G B
B G B G o G B
B G B G B G o
B G B G B o G
B G B o B G G
B o B G B G G
B B o G B G G
B B B G o G G
B B B o G G G
Key:
B = Brown frog
G = Green frog
O = Empty lilypad
If you read this, it should explain the movements of each frog.
E.R.
1. It takes a minimum number of moves of 16. I got this by doing this……
G G G O B B B
G G O G B B B
G G B G O B B
G G B G B O B
G G B OB G B
G O B G B G B
OG B G B G B
B G O G B G B
B G B G O G B
B G B G B G O
B G B G B O G
B G B O B G G
B O B G B G G
B B O G B G G
B B B G O G G
B B B O G G G
KEY
B=brown frog
G= green frog
O= empty lily pad
SK WO
G=GREENFROG
B=BROWN FROG
E=EMPTY SPACE
GGGEBBB
GGGBEBB
GGEBGBB
GEGBGBB
GBGEGBB
GBGBGEB
GBGBGBE
GBGBEBG
GBEBGBG
EBGBGBG
BEGBGBG
BBGEGBG
BBGBGEG
BBGBEGG
BBEBGGG
BBBEGGG
1. The minimum number of moves to have the different color frogs change place is 15 in my guess. The sequence above shows the difference between each move to show how we swapped the frog spaces.
A.W.
I got a total of 16 moves; I got this answer by making 7 boxes on a piece of paper. Then, I made one an empty box and put green frogs on one side and brown frogs on the other side. And every time I made a move, I put one number down for that move. When I moved a frog, I erased it and put in the box I want it to go into. I kept doing this until I got all the frogs in the right places in order to complete this question. And that is how I got this answer.
A.L.
I got a total of 16 moves. So I made 7 boxes. I made a line on each side of the empty box. Then I wrote Green above the right boxes and Brown above the left boxes. For green I put a circle in each one of the boxes under green and then for brown I did the same except I made one line.
So every time I moved a frog I wrote down a one under all of the boxes to keep track of how many time I moved something. Every timed I moved a frog I erased that frog and erased that frog if there was one but I kept on moving all those frogs until the empty box was empty and the opposite color was on the opposite side. I double checked this problem by doing it again because I was helping A.W. because she didn’t get. So by then I double checked it and got 16 once again.
1. If the girls stop when they have made the same number of invitations it would be 1:00 and they would have made 60 invitations. The way I got that answer is , I made a table that went up to one o clock. The # of invitations I got for that was 60
2. Together they would have written 120 invitations. I got this by adding 60 and 60 together.
3. The # of people that will attend the party is 26. I got this by adding 120 and 120, because one invitation is for two people. Then I divided 240 by three to find out one third of it. Then I added 13 and 13 to get two thirds.
mb
1. If the girls stop when they have written the same number of invitations, it would be 1:00, and they would have made 60 invitations. The way I answered was that I used a table, and it showed that when it was 1:00, they both made 60 invitations.
Together, they would have written 120 invitations. They way I got my answer was that I added 60+60 and got 120. The number of people that attend the party would be 26. I got this answer by multiplying 120 by 2. Then I divided 240 by three, because 120x2=240, to find out 2 thirds of it. The answer to that was 13. So, I added 13 and 13 and got 26, which would be two thirds, and got that answer.
Bt
Hoppy days
It takes 15 moves to make the frogs switch spots.
MB
MJS
1. The minimum number of jumps are 15 jump.
2. You will started with the brown frog and ended with the brown frog.
J.M.
1. The minimum number of hops they can have is 15.
2. You will start with the brown frog and end with the brown frog.
1. The minimum number of frogs is 15 hops.
2. You will start with the brown frog and end with the brown frog.
BV and MV.
MG
It takes 15 frogs at minimum to get each one to the other side. The way they move is that they jump over each other, they go left and right and two frogs can’t stand on one pad at a time. So they jump over each other when there is an open space available.
C.D.
My number of hops was 16. The way I got this was I drew 7 squares. In the first 3 I drew circles, 4th nothing; in the 5-7 squares I drew lines. Every time I would get a line in a empty, circle. Square or vice versa I would keep it there. Every time I would make a move I would count it as one hope.
AM
You need a total of 15 moves for the frogs to switch. I am going from right to left. First click the 3rd green frog, click the 1st brown frog, then the 2nd brown frog, then the 3rd green frog, click the 2nd green frog, after that click the 1st green frog, then click the 1st brown frog, click the 2nd brown frog, and then click the 3rd brown frog, then click the 3rd green frog followed by the 2nd green frog and the 3rd green frog, after that click the 2nd brown frog followed by 3rd brown frog, then finally click the 1st green frog and you have gotten the green frogs and the brown frogs to switch.
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