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Permutations And Combinations
Let the total number of stones be 2n + 1
∴ There are n stones on each side of the middle stone. Let the man starts collecting stones from the extreme left stone. The distance covered by man to bring the extreme left stone to the middle stone = 10n metres. The distance covered by man to bring the (n  1)th stone on left to the middle stone = 2 10 (n  1) metres.
∴ The total distance covered by the man to bring all the stones from left to the middle stone
= 10n + 20(n  1) + 20(n  2) + ......... + 20
Similarly, the total distance covered by the man to bring all the stones from the right to the middle stone
= 20 + 20 (n  1) + ......... + 20
∴ Total distance covered by the man to bring all the stones to the middle stone
= 30n + 40 (n  1) + 40 (n  2) +........ + 40 (1)
= 40 [n + (n  1) + (n  2) + ....... + 1]  10n =
But the distance covered is 3 km or 3000 metres.
∴
n = 12
∴ Number of stones = 2(12) + 1 = 25
Sponsor Area
Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.
Sponsor Area