## What is the answer for this question?

Sorry if this is a stupid question (horrible at math), but how many $$x$$‘s are there in:

$$frac{1}{2}x + frac{1}{2}x + frac{1}{2}x$$

I think that answer is $$3$$, but the answer isn’t correct.

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## Sum of a sequence that has an answer, but I can’t get that answer by hand

Find n if

$$a_1 = 4$$

$$r = -4$$

$$S_n = 13108$$

Using the formula

$$S_n = frac{a_1(1 – (r)^n)}{1 – r}$$ I would have

$$13108 = frac{4(1 – (-4)^n)}{5}$$

$$65540 = 4(1 – (-4)^n)$$

$$16385 = 1 – (-4)^n$$

$$16384 = -(-4)^n$$

$$-16384 = (-4)^n$$

I can’t take the log now though because I have negatives! I know the answer is 7 because if I plug in n = 7, I do get the desired result. However, I’m not sure how to get this by hand. Can someone please clear this up?

## python – CodeChef showing wrong answer for my below submission, but my code is working perfect in VSCode

The game of billiards involves two players knocking 3 balls around on a green baize table. Well, there is more to it, but for our purposes this is sufficient.

The game consists of several rounds and in each round both players obtain a score, based on how well they played. Once all the rounds have been played, the total score of each player is determined by adding up the scores in all the rounds and the player with the higher total score is declared the winner.

The Siruseri Sports Club organises an annual billiards game where the top two players of Siruseri play against each other. The Manager of Siruseri Sports Club decided to add his own twist to the game by changing the rules for determining the winner. In his version, at the end of each round the leader and her current lead are calculated. Once all the rounds are over the player who had the maximum lead at the end of any round in the game is declared the winner.

• Input:
The first line of the input will contain a single integer N (N≤10000) indicating the number of rounds in the game. Lines 2,3,…,N+1 describe the scores of the two players in the N rounds. Line i+1 contains two integer Si and Ti, the scores of the Player 1 and 2 respectively, in round i.

• Output:
Your output must consist of a single line containing two integers W and L, where W is 1 or 2 and indicates the winner and L is the maximum lead attained by the winner.

Consider the following score sheet for a game with 5 rounds:

• Sample input:
• 5
• 140 82
• 89 134
• 90 110
• 112 106
• 88 90
• Sample output:

1 58

``````import sys
scores = ()
winner = 0
noOfRounds = 0
compareCount = 0
noOfRounds = int(input())

if(noOfRounds < 1 or noOfRounds > 10000):
sys.exit()

for i in range(noOfRounds):
scores.append(list(map(int, input().split())))
if(scores(i)(0) < 1 or scores(i)(0) > 1000 or scores(i)(1) > 1000 or scores(i)(1) < 1):
sys.exit()

for j in range(noOfRounds):
if(scores(j)(0) > scores(j)(1)):
scores(j)(1) = scores(j)(0) - scores(j)(1)
scores(j)(0) = 1
elif(scores(j)(0) < scores(j)(1)):
scores(j)(1) = scores(j)(1) - scores(j)(0)
scores(j)(0) = 2
else:
continue

k=0
for z in range(1,noOfRounds):
if(scores(k)(1) > scores(z)(1)):
winner = scores(k)
elif(scores(k)(1) < scores(z)(1)):
winner = scores(z)
k+=1
else:
continue

if(noOfRounds == 1):
print(*scores(0))
else:
print(*winner)
``````

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