Riddle:
How many months have twenty-eight days?
Answer: All twelve months have 28 days.
Riddle:
Two schoolgirls were traveling from the city to a dacha (summer cottage) on an electric train.
"I notice," one of the girls said "that the dacha trains coming in the opposite direction pass us every 5 minutes. What do you think-how many dacha trains arrive in the city in an hour, given equal speeds in both directions?"
"Twelve, of course," the other girl answered, "because 60 divided by 5 equals 12."
The first girl did not agree. What do you think?
Answer: If the girls had been on a standing train, the first girl's calculations would have been correct, but their train was moving. It took 5 minutes to meet a second train, but then it took the second train 5 more minutes to reach where the girls met the first train. So the time between trains is 10 minutes, not 5, and only 6 trains per hour arrive in the city.
Riddle:
When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101.
Answer: 50 X 101=5,050.
What is the sum of all the digits in integers from 1 through 1,000,000,000? (That's all the digits in all the numbers, not all the numbers themselves.)
Answer: The numbers can be grouped by pairs:
999,999,999 and 0;
999,999,998 and 1'
999,999,997 and 2;
and so on....
There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then:
(500,000,000 X 81) + 1= 40,500,000,001.
Riddle:
A soccer fan, upset by the defeat of his favorite team, slept restlessly. In his dream a goalkeeper was practicing in a large unfurnished room, tossing a soccer ball against the wall and then catching it.
But the goalkeeper grew smaller and smaller and then changed into a ping-pong ball while the soccer ball was swelled up into a huge cast-iron ball. The iron ball circled round madly, trying to crush the ping-pong ball, how did the ping-pong find safety whithout leaving the floor?
Answer: If the ping-pong ball rolls flush against the wall, the cast-iron ball cannot crush it.
Those who know geometry can determine that if the diameter of a large ball is at least 5.83 (3+2(square root of 2) times as large as the diameter of a little ball, then the little ball will be safe if it hugs the wall.
A cast-iron ball that is larger than a soccer ball is more than 4.83 times as large in diameter as a ping-pong ball.
Riddle:
As I traveled up and down our great glorious country, I found myself in a place where the tempature goes up sharply in the day and down at night. This had an effect on my watch, I noticed it was 1/2 a minute faster at nightfall, but at dawn it had lost 1/3 minute, making it only 1/6 minute fast.
One morning- May 1- my watch showed the right time. By what date was it 5 minutes faster?
Answer: In 24 hours the watch gained 1/2-1/3= 1/6 minute. It would seem it would be 5 minutes fast in 5 X 6= 30 days; that is,the morning of May 31. But already on the morning of May 28 the was 27/6= 4 1/2 minutes fast. At the close of the day the watch gained 1/2 minute more, so it was 5 minutes fast on may 28.
Riddle:
A house has 6 stories, each the same height. How many times as long is the ascent to the sixth floor as the ascent to the third?
Answer: 2 1/2 times (5/2, not 6/3).
Riddle:
What arithmetic symbol can be put between 2 and 3 so that the resulting number is greater than 2 but less than 3?
Answer: A decimal point. 2.3 is greater than 2 and less than 3.
Riddle:
A half is a third of it. What is it?
Answer: 1 1/2.
Riddle:
Twelve flags stand equidistant along the track at the stadium. The runners start at the first flag. A runner reaches the eighth flag 8 seconds after he starts. If he runs at an even speed, how many seconds does he need altogether to reach the twelfth flag?
Answer: Not 12 seconds. There are 7 segments from the first flag tot the eighth, and 11 from the first to the twelfth. He runs each segment in 8/7 seconds; therefore, 11 segments take 88/7= 12 4/7 seconds.
Riddle:
An alarm clock runs 4 minutes slow every hour. It was set right 3 1/2 hours ago. Now another clock which is correct shows noon.
In how many minutes, to the nearest minutes, to the nearest minute, will the alarm clock show noon?
Answer: In 3 1/2 hours the alarm clock has become 14 minutes slow. At noon the alarm clock will fall behind approximently an additional minute. Its hands will show noon in 15 minutes.
