June 2021

A man and his wife invite 8 of their friends to a dinner. They are to be seated around a round table. How many arrangements can be made if the man and his wife are to sit side by side?

The local weather forecaster says “no rain” and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data available, what is the chance of rain?

A man passed one-sixth of his life in childhood, one-twelfth in youth, and one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father at half his father’s final age. What was the man’s final age?

Three people toss a coin, and the odd man pays for the coffee. If the coins all turn up the same, they are tossed again. Find the probability that fewer than 4 tosses are needed.

A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?

Two casks A and B were filled with two kinds of sherry. In cask A, the ratio of the two kinds of sherry is 2:7 while in B, it is 1:5. How many gallons will be taken from each cask to form a mixture which shall consist of 2 gal of one kind and 9 gal of the other?

A coin is so unbalanced that it may come both heads in 2 tosses as it may come tails in a single toss. What is the probability of getting a head in a single toss?

Ted on his bicycle and Noli on his motorcycle started to move simultaneously at 8:00 am from points A and B on a road toward each other. Each is moving at his own constant speed. They met at noon (12 o'clock at midday) and continued to move without stopping each on his way at the same speed. Noli arrived to point A at 2:00 pm. At what time Ted arrived to point B?

A farmer owned a square field measuring exactly 2261 yards on each side. 1898 yards from one corner and 1009 yards from an adjacent corner stood a beech tree. A neighbor offered to purchase a triangular portion of the field, stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the beech tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. How long was the fence?

A man arrives at the railroad station nearest his country home an hour and 5 minutes before the time at which he had ordered his driver to meet him with his car. He starts to walk at the rate of 4mph and meets his car when it has traveled 8 miles. It turns back and takes him the remainder of the way home, where he arrives just 10 minutes ahead of the time he had originally planned to get there. Find the distance from the station to his home. Assume no waiting time on the part of his driver.