In a college fest, a treasure hunt was organised where in 16 objects numbered 1 through 16 were placed in various places of the college campus. All 16 objects are placed at the intersection of tracks that crisscross the campus. The treasure map of the objects is as follows and every participant has a copy of it. You can go from one object to the other only along the parallel tracks.Akash took part in the Treasure Hunt. Any object that he encounters is identified as a1 or a2 or…if it is the 1st or the 2nd or …object that he picked up. The last object is indicated as an and it means that Akash has managed to pick n objects.For instance if Akash’s sequence of objects identified in his hunt are: 14 – 4 – 7 – 15 – 10 it means a1 = 14, a2 = 4, a3= 7 and an= 10. In this case n = 5.Other rules of the treasure hunt make this also a game of chance. The rules are:(i) Akash has to pick a chit from a lot of 16 chits. The chit that he picks is his a1.(ii) When an object is encountered, it must be picked up. When it is picked up, that object disappears from the map of treasure hunt with the participant.(iii) After an object is picked up, Akash can change his direction of motion only once i.e., he has to either continue to move straight or turn 90 degrees either to the left or to the right. He is not allowed to reverse the direction of his motion.Question No 36.For Akash if an = 6. If an-1 = 7, then how many possible sequences are there?
Question
In a college fest, a treasure hunt was organised where in 16 objects numbered 1 through 16 were placed in various places of the college campus. All 16 objects are placed at the intersection of tracks that crisscross the campus. The treasure map of the objects is as follows and every participant has a copy of it. You can go from one object to the other only along the parallel tracks.Akash took part in the Treasure Hunt. Any object that he encounters is identified as a1 or a2 or…if it is the 1st or the 2nd or …object that he picked up. The last object is indicated as an and it means that Akash has managed to pick n objects.For instance if Akash’s sequence of objects identified in his hunt are: 14 – 4 – 7 – 15 – 10 it means a1 = 14, a2 = 4, a3= 7 and an= 10. In this case n = 5.Other rules of the treasure hunt make this also a game of chance. The rules are:(i) Akash has to pick a chit from a lot of 16 chits. The chit that he picks is his a1.(ii) When an object is encountered, it must be picked up. When it is picked up, that object disappears from the map of treasure hunt with the participant.(iii) After an object is picked up, Akash can change his direction of motion only once i.e., he has to either continue to move straight or turn 90 degrees either to the left or to the right. He is not allowed to reverse the direction of his motion.Question No 36.For Akash if an = 6. If an-1 = 7, then how many possible sequences are there?
Solution
The problem is asking for the number of sequences that end with 7 and then 6. Given the rules of the game, Akash can only reach 6 from either 7, 11, or 15. However, since an-1 = 7, we know that he must have reached 6 from 7.
Therefore, the problem reduces to finding the number of sequences that end with 7.
Looking at the map, Akash can reach 7 from either 3, 4, 11, or 12.
If Akash reaches 7 from 3, then he could have reached 3 from either 2 or 4.
If Akash reaches 7 from 4, then he could have reached 4 from either 3, 8, 14, or 15.
If Akash reaches 7 from 11, then he could have reached 11 from either 6, 7, 12, or 16.
If Akash reaches 7 from 12, then he could have reached 12 from either 7, 11, or 13.
Continuing in this manner, we can see that the problem involves a lot of recursion and would be best solved using dynamic programming.
However, without a map or further information, it's impossible to provide a numerical answer.
Similar Questions
a maze using prepositions to reach the treasure at the end.
With the teacher’s help, children design a treasure hunt for the younger children, leaving clues around the outdoor play area and drawing a map.Mixed-agedPreschoolersSchool-agersSpecial needsInfantsToddlers
Imagine you are exploring a treasure map🗺️ in a game. Here is the starting coordinates and sets of instructions. Can you identify the final location 🏴☠️ of the hidden treasure?Starting Point: (1, 4)Instructions: Move 3 units to the right and 2 units down.
What is Mongoose?*2 pointsAn object document mappingA small terrestrial carnivorousAn object-relational mapping
Every object in a bucket is associated with one unique____?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.