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Hint: Work out the runs for the total number of innings.
Answer: 6 runs per innings.
After the initial 32 innings, 32 x 11 = 352 runs had been made.
After 40 innings the average was now 10, which means a total of 400 runs.
So an extra 48 runs were made in the last 8 innings, an average of 6 runs per innings. QED.
Puzzle 1215
If today is Monday, what is the day after the day before the day before tomorrow?
[Ref: ZUTR]
Hint: Think carefully.
Answer: Monday.
Puzzle 1216
I have two children. At least one of them is a boy.
What is the probability that both my children are boys?
My sister also has two children. The older child is a girl.
What is the probability that both her children are girls?
[Ref: ZFCA]
Hint: Before we're told anything, there are four possible combinations.
Answer:
If we list the possible combinations before we're told anything, and listing the eldest child first we have 4 possible outcomes:
BoyBoy
BoyGirl
GirlBoy
GirlGirl
Since I have two children, and we know that at least one is a boy, there are three equally probable cases: BoyBoy, BoyGirl or GirlBoy. In only one case are both children boys, so the probability that both are boys is 1 in 3.
My sister's situation is different. Knowing that the older child is a girl, there are only two equally probable cases: GirlGirl or GirlBoy. Therefore the probability that both children are girls is 1 in 2.
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