#132 One of these days
Dear class,
I told you that we would have a quiz next week, and many of you have asked on which day it will be given. An understandable question, so I have helpfully provided the answer below.
A: The quiz will be on Friday, or else Tuesday.
B: The quiz will be on either Monday or Thursday.
C: Either statement B or D is false, but not both.
D: Either the quiz is on Monday or Wednesday, or exactly two of statements A to E are true.
E: Either the quiz is on Tuesday or Thursday, or more than two of statements A to E are false.
Hope that helps.
Your favourite maths teacher,
Mr Gordon
#131 The Paradise Club
Solution
1/18; 18/35.
The total T when adding the scores of two regular dice ranges from 2 to 12. Also, T has the same chance of appearing as 14-T (opposite die faces add up to 7, making 14 for two dice), so 3 and 11 are equally likely, as are 4 and 10 and so on. The only values of T for which both T and 14-T are different primes are 3 and 11. Of the 36 possible combinations of two dice, only two add to 3, so the chance of scoring 3 (or 11) is 2/36 or 1/18.
Let鈥檚 call Gus鈥檚 chance of a free drink G. He either wins first go (a 1/18 chance) or he fails and Bart fails, returning us to where we started and his chance is G. So G=1/18+(17/18)脳(17/18)G. Solving this gives G=18/35.
Quick quiz #120
1 Which element gets its name from an ancient Greek word meaning 鈥渢o lie hidden鈥�?
2 In what year was the first recorded circumnavigation of Earth completed?
3 Where would you find the Colombo, Maxwell, Bond and Dawes gaps?
4 Which of the following is an essential amino acid: tryptophan, alanine or asparagine?
5 The Einstein Cross is an example of which astronomical object?
Answers
1 Lanthanum. It is derived from the ancient Greek word lanthanein
2 1522
3 Between Saturn鈥檚 rings
4 Tryptophan
5 A quasar