In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Possible total lengths:
6+5+6 = 17.
6+5+6+5+6 = 3*6 + 2*5 = 28.
6+5+6+5+6+5+6 = 4*6 = 3*5 = 39.
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Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the below diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
There are different things like p,q,r,s,t,u,v. We can take p and q together. If r and s are taken together then t must has to be taken. u and v can be taken together.v can be taken with p or s. every thing can be taken together except
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The Maximum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack.
Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
AIn order to win, Alice's first move should be a 1-move.
BIn order to win, Alice's first move should be a 0-move.
CIn order to win, Alice's first move can be a 0-move or a 1-move.
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