Li'l Turtle wrote, "I heard she was having a crazy sale!"
I just love yard sales. I am on my way.
For those who've never been there, no explanation is possible....... For those who have, no explanation is needed..........
"Void where prohibited and only while supplies last."
Bring it on!
Mark, you are my hero.
17) B
18) D
21) B
23) D
17. (B) Team A can win in the following circumstances representing the order of wins after the first game: AA, ABA, ABBA, BAA, BBAA, BABA. These sequences of wins for A have probabilities [1/4], [1/8], [1/16], [1/8], [1/16], [1/16], respectively. Adding them provides the answer.
18. (D) Let the first number of the consecutive sequence be F, and let the last number be L. Then, if there are n numbers in the sequence, 75 = n[(F+L)/2] > 150 = n(F+L). Now n, F and L are positive integers and thus n divides 150 = 2×3×5×5. Thus possible values of n are 2,3,5,6,10,15,... The following table sets out the possibilities
n F+L SUM
2 75 37+38
2 50 24+25+26
5 30 13+14+15+16+17
6 25 10+11+12+13+14+15
10 15 3+4+5+....+10+11+12
For n = 15 or more F would be negative. Thus there are 5 possible values of n.
21. (B) Simplifying the expression we have 12a+12b = ab- ab-12a-12b+144 = 144- a(b-12)-12(b-12) = 144 - (a-12)(b-12) = 144. (The table will not reproduce)
The last in this file, thank goodness.
You are at a computer store which sells 3 computers: the Japanese one, which always answers any Yes-or-No question correctly, the Chinese one, which always answers any Yes-or-No question IN-correctly, and a Russian one, which sometimes tells the truth and sometimes lies - you never know.
You can ask one Yes-or-No question to any one of the three computers, after which you must buy any one of the three. You don't want the Russian computer, but each of the other two is okay. What can you do
N cars, each having a different speed, are going along a 1-lane road, so no passing is possible. Eventually, the cars will accumulate in packets, with the "fast" cars tailgating the "slow" ones. E.g., if the initial order was 1,5,2,4,3 (1 being the slowest, 5 being the fastest), we will end up with 3 packets: {1}, {5,2} and {4,3}. can you find the average number of packets as a function of N.
A family of 4 is trying to cross a bridge at night. One needs a flashlight to cross the bridge, and only two persons can cross the bridge at the same time, moving at the speed of the slower of the two. Father crosses the bridge in 1 minute, Mother in 2 minutes, Child in 5 minutes and Granny in 10. What is the fastest way for them to cross the bridge
The obvious solution is for F to always carry the flashlight back, i.e., FM+F+FC+F+FG which means 19 minutes (the notation means: first, F and M cross, then F carries the flashlight back, third, F and C cross together, fourth, F carries the flashlight back again, finally, F and G cross). Can you do faster
It is alleged that this is the standard problem given at an interview at M*soft.
Starting tomorrow HARDCORE RIDDLES.
Not for the faint hearted, or those on medication.
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If you read this far you must be a lawyer trying to find a loophole in this disclaimer, or you just cheated and checked the end to see what I added here. I should have put this in the middle somewhere. Be happy. Rock on.
