Magical Pond (Difficult Case)

Transcript

Magical Pond (Difficult Case)There is another pond in which the number of lotuses triples every day. When both the ponds had no flowers, Damayanti placed a lotus in the doubling pond. After 4 days, she took all the lotuses from there and put them in the tripling pond. How many lotuses will be in the tripling pond after 4 more days? First 4 days, Lotuses are in Doubling pond Then, Day 5 to 8 (next 4 days), lotus are in Tripling pond Let’s find out how to go about it, Number of lotus in Doubling pond after Day 1 = 1 Number of lotus in Doubling pond after Day 2 = 2 × 2 = 22 Number of lotus in Doubling pond after Day 3 = 22 × 2 = 22+1 = 23 Number of lotus in Doubling pond after Day 4 = 23 × 2 = 23+1 = 24 Now, all lotuses (24) go to tripling pond Number of lotus in Tripling pond after Day 5 = 24 × 3 Number of lotus in Tripling pond after Day 6 = (24 × 3) × 3 = 24 × 32 Number of lotus in Tripling pond after Day 7 = (24 × 32) × 3 = 24 × 33 Number of lotus in Tripling pond after Day 8 = (24 × 33) × 3 = 24 × 34 Thus, Total Lotuses after Day 8 = 24 × 34 = (2 × 3)4 = 64 We have another question What if Damayanti had changed the order in which she placed the flowers in the lakes? How many lotuses would be there? The answer would be Total Lotuses after Day 8 = 1 × 34 × 24 = 34 × 24 = (3 × 2)4 = 64