A stone insurance is considered to be an authentic source of histor
Answers
ANSWER
A
n
A
n−1
... A
1
M B
1
... B
n−1
B
n
Let the number of stones at each side of the middle stone be n (i.e., total of 2n+1 stones)
Let M be the middle stone, A
1
...A
n
be the stones at the left, B
1
...B
n
be the stones at the right
Consider he picks the stone B
1
and brings it back to the middle. Distance traveled =2×10
Then he picks the stone B
2
and brings it back to the middle.
Distance traveled =2×2×10
For B
3
, distance traveled =2×3×10.
...
For B
n
, distance traveled =2×n×10
Total distance traveled for bringing back all the stones at the right
=2×10+2×2×10+2×3×10+...+2×n×10
=2×10[1+2+...+n]
Then he picks A
1
and returns. Same pattern is continued.
Distance traveled to bring back all the stones at left will be same as 2×10[1+2+...+n]
Total distance traveled=2×2×10[1+2+...+n]
⇒ 2×2×10[1+2+...+n]=4800
⇒ [1+2+...+n]=120
⇒
2
n(n+1)
=120
⇒ n(n+1)=240
⇒ n
2
+n−240=0
⇒ (n+16)(n−15)=0
⇒ n=15 ( Negative value not possible )
⇒ Number of stones =2n+1=2×15+1=31