Question

Ten kangaroos are placed as shown in the image. The kangaroos that are next to each other and that are looking at each other switch places. The procedure is done until any kangaroo can switch places. How many switches are made?​

Answer 1

Solution :-

Position of 10 kangaroos :-

K1 > K2 > K3 > < K4 < K5 K6 > K7 > K8 > < K9 < K10

Case 1) :- Next to each other and that are looking at each other switch places ,

K1 > K2 > < K4 K3 > < K5  K6 > K7 > < K9 K8 > < K10

• Number of switches = 2

Case 2) :- same process,

K1 > < K4 K2 > < K5 K3 > K6 > < K9 K7 > < K10 K8 >

• Number of switches = 4

Case 3) :-

< K4 K1 > < K5 K2 > K3 > < K9 K6 > < K10 K7 > K8 >

• Number of switches = 4

Case 4) :-

< K4 < K5 K1 > K2 > < K9 K3 > < K10 K6 > K7 > K8 >

• Number of switches = 3

Case 5) :-

< K4 < K5 K1 > < K9 K2 > <K10 K3 > K6 > K7 > K8 >

• Number of switches = 2

Case 6) :-

< K4 < K5 < K9 K1 > < K10 K2 > K3 > K6 > K7 > K8 >

• Number of switches = 2

Case 7) :-

< K4 < K5 < K9 < K10 K1 > K2 > K3 > K6 > K7 > K8 > .

• Number of switches = 1

therefore, we can conclude that, total 18 switches are made .

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