Sentence to Freedom

A peasant is convicted in China. He gets the death penalty. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If the peasant lies, he will be hanged. If he speaks the truth he will be beheaded. The peasant speaks a last sentence and everybody surprise some minutes later he is get free because the judge cannot determine his penalty. What did the peasant said?

SOLUTION :

The peasant said:"I shall be hanged!". -QED-

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It's always

It's always 1 to 6
it's always 15 to 20
it's always 5
but it's never 21
and if 21, it's flying.

SOLUTION :
a dice.
It's always 1 to 6 : the numbers on the faces of the dice,
it's always 15 to 20 : the sum of the exposed faces when the dice comes to rest after being thrown,
it's always 5 : the number of exposed faces when the dice is at rest,
and if 21 it's flying : the run of all exposed faces when the dice is flying.

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Math's Sentences

In this sentences. There is ... The numbers of 0. And ... The numbers of 1. And ... The numbers of 2. And ... The numbers of 3. And ... The numbers of 4. And ... The numbers of 5. And ... The numbers of 6. And ... The numbers of 7. And ... The numbers of 8. And ... The numbers of 9.

SOLUTION :

Respectively 1 7 3 2 1 1 1 2 1 1. -QED-

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Trains

A train leaves Los Angels for New York every hour on the hour. A train leaves New York for Los Angels every hour on the half hour. The trip takes five hours each way.
As you ride from Los Angels to New York, how many of the trains bound from New York to Los Angels would you pass?

SOLUTiON :

You would pass the first train returning to Los Angels fifteen minutes after you start(you are fifteen minutes out of Los Angels and the other train is due in Los Angels fifteen minutes later) and one each half hour there after.
You will pass ten trains bound for Los angels. -QED-

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Time

Simpkins and Green made arrangements to meet at the railroad station to catch the eight o'clock train to Philadelphia. Simpkins thinks that his watch is twenty five minutes fast although it is in fact ten minutes slow. Green thinks his watch is ten minutes slow, while it actually has gained five minutes.
What will happen if both men, relying upon their watches, try to arrive at the station five minutes before train time.

SOLUTION :

Simpkins thinks he will be in plenty of time when his watch shows 8:20, but it is already 8:30, much too late to catch the train. But Green will reach the station when his watch shows 7:45, and since his watch is five minutes fast, he will really be there at 7:40, twenty minutes ahead of train time. -QED-

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Window Washing

When Mr.Watson built his home, he made one wall of the living room entirely out of thick plate glass. He soon realized how expensive as well as inconvenient it was to live in a "glass fishbowl", for the glass had to be washed on the average of once a week. It was too big a job for him, since the wall measured nineteen by twenty feet, so he contracted with a window cleaning service to do the full job once a week at the cost of one dollar per hundred square feet of surface washed, what was Watson weekly bill?

SOLUTION :

The "full job" would have to include both the inside and outside 2 times 19 times 20 equals 760 square feet of surface to be washed. The bill was thus $7.6 per week. -QED-

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The Empty Flask

An apothecary found six flasks capable of holding sixteen, eighteen, twenty-two, twenty-three, twenty-four, and thirty-four fluid ounces respectively. He filled some with distilled water and then filled all but one of the rest with alcohol, nothing that he had used twice as much alcohol as water.
Which flask was left over? And which flasks were used for distilled water, which for alcohol?

SOLUTION :

Since the apothecary had used twice as much alcohol as water, the total ounces of alcohol and water together must be divisible by 3. The total capacity of all 6 flasks is 137 ounces, a number which is 2 more than a multiple of 3. Because the apothecary left one flask empty, it is obvious that this flask must have had a capacity in ounces which is 2 more than a multiple of 3. The only flask which meets this requirement is the one with a capacity of 23 ounces. This flask must have been the one left empty. The remainder, which have a combined capacity of 114 ounces, were filled. One-third of this total, 38 ounces, was water. The 16 and 22-ounces flasks must therefore have been used for water and the 18, 24, and 34-ounce flasks used for alcohol. -QED-

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Rare Flowers

It was a day of special joy for Mrs. Greenhouse. She was exhibiting her collection of rare flowering plants to members of her garden club.
"Now these are my real treasures," she said in her best lecture voice, pointing to three luxuriously flowering specimens. "I got them from Guatemala only a year ago, and I have been giving them my closest attention. They are all quite delicate indeed. Since the flowers last only a single day. The plant with crimson flowers blossoms every fourth day, but I have to wait until the seventh day for the plant with lavender flowers. But that one is the most precious of all," she said, directing attention to her third plant."It takes a full thirteen days for it to blossom."
Since her three tropical flowering plants were such an enormous attraction, Mrs. Greenhouse expansively invited the club members to return to see them again."Let's make it next year on this very same day," she announced, "since they will all be in blossom them."
Was Mrs. Greenhouse correct in her horticultural reckoning?

SOLUTION :

If the club members come a year later on the very same day of the month, they would be one day later for the triple blooming. On the other hand, if they come next year on the very same day of the week(and as nearly as possible a year later), they would be right on time.
The least common multiple of 4, 7, and 13 is the smallest number divisible by all three numbers. Since this number is 4x7x13=364, it can be seen that the three plants blossom simultaneously every 364 days-52 weeks, but one day less than a full year. -Q.E.D-

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