## November 2016 Problem

In a dancing school, some students do not have a permanent dancing partner : this concerns 2/7 of the girls and ¼ of the boys. What percentage of the students has a permanent dancing partner ?

In a dancing school, some students do not have a permanent dancing partner : this concerns 2/7 of the girls and ¼ of the boys. What percentage of the students has a permanent dancing partner ?

Jack picks at random three integers between 7 and 11 (inclusive). Mary picks an integer from 24 to 33 (inclusive). What is the probability that Mary’s number is less than the sum of Jack’s numbers ?

A stock of 650 tons of wood has a 16% moisture content. A month later, as a result of drying, the moisture content reduced to 9 %. What is the new weight of the stock?

A postman has to distribute 10 identical postcards to 5 mailboxes. By how many ways can he do this ?

Ten students are standing in line. How many possibilities do we have to select four out of them, so that no two were neighbors in this line?

One year, August has 4 Wednesdays and 4 Sundays.

How many Mondays does this year have?

Using numbers 1,2,3,6 and 12 (once each) and operations of subtraction and division, obtain 36.

A group of tourists has a lunch. Two different jars of apple juice and of strawberry juice are put on the table.

Each tourist takes a 200-ml glass of fruit cocktail, mixing both juices at random. Jack takes a sixth of the apple juice amount and an eighth of the strawberry juice amount. Every glass contains both juices. How many people are in the group?

Find the sum of the digits in the number 16^{43} x 3125^{34 }

Given *a*^{2 }+ 1 + a^{-2} = a + a^{-1 }
Without calculating *a*, find the value of *a*^{129 }- a^{128} + a^{127} - a^{126} = ?

How can you make a number ABCDE 100001 times bigger without doing any mathematical operations?

A rich merchant left a testament:
If my wife delivers a boy, after my death she receives 1/4 of my property and my son - 3/4.
If this is a girl, my wife receives 3/4 and my daughter - 1/4.
A week after the merchant passed away, his wife delivered twins - a boy and a girl.
How will you share the heritage between them, respecting the merchant's will?