## May 2016 Problem

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?

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?

128 players start a tennis tournament. How many matches will be played ?Answer through reasoning, without any calculations.
-----------------------------------------------------------------------------------------------------------------------

Dear visitors,

thank you for sending me your solutions. Many of them were correct, but not optimal. ------------------------------------------------------- Here is the solution: The goal of the tournament is to eliminate 127 players. For this you need 127 matches. Thus, 127.With best wishes

Serge Hazanov