Question 5 - Supercells - Chapter 3 Class 6 - Number Play (Ganita Prakash)

Transcript

Question 5 Find out how many supercells are possible for different numbers of cells. Do you notice any pattern? What is the method to fill a given table to get the maximum number of supercells? Explore and share your strategy.Yes, there is a clear pattern and a repeatable strategy. The Pattern The maximum number of supercells you can have depends on whether the number of cells (N) is even or odd. If N is an odd number: The maximum number of supercells is (N + 1) / 2. For 3 cells: (3 + 1) / 2 = 2 supercells For 5 cells: (5 + 1) / 2 = 3 supercells For 9 cells: (9 + 1) / 2 = 5 supercells If N is an even number: The maximum number of supercells is N / 2. For 2 cells: 2 / 2 = 1 supercell For 4 cells: 4 / 2 = 2 supercells For 8 cells: 8 / 2 = 4 supercells The Method (Strategy) The method to always get the maximum number of supercells is as follows: Determine the number of "high" and "low" numbers you need. For N cells, you will need (N+1)/2 high numbers if N is odd, or N/2 high numbers if N is even. The rest will be low numbers. Select your numbers. Choose two sets of numbers. The "high set" must contain numbers that are all numerically larger than every number in the "low set". Arrange the numbers. Fill the table by alternating between the two sets, starting with a number from the high set. The arrangement will be: [High, Low, High, Low, High, ...]. This ensures that every number from the high set is surrounded by smaller numbers, making it a supercell.