Complex Problems

This is a commonly known chess problem...

Thanks to Mike and Ruth VanderMeer from Canada, we can present you the following names and numbers puzzle:

Four words add up to a fifth word numerically:

     mars
    venus
   uranus
   saturn
  -------- +
  neptune

Each of the ten letters (m, a, r, s, v, e, n, u, t, and p) represents a digit in the range 0 up to 9 (equal letters represent equal digits and different letters represent different digits). Furthermore, the digits 1 and 6 are being used most frequently.

This is the toughest number net on our site! It has nineteen circles that have to be filled with the numbers 1 up to (and including) 19. These numbers have to be placed in such a way that all numbers on any horizontal row and any diagonal line add up to the same sum.

Warning: there are many horizontal and diagonal lines, which have a different number of circles (3, 4, or 5), nevertheless all these sums have to be equal!

Thanks to Lucas Jones we can present you the following puzzle:

A man is going to an Antique Car auction. All purchases must be paid for in cash. He goes to the bank and draws out $25,000.

Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15. Each envelope contains the least number of bills possible of any available US currency (for example, no two tens instead of a twenty).

At the auction he makes a successful bid of $8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount.

In an alley two ladders are placed cross-wise. The lengths of these ladders are resp. 2 and 3 meters. They cross one another at one meter above the ground.

Four white pieces (the mice) are placed on one side of a chessboard, and one black piece (the cat) is placed at the opposite side. The game is played by the following rules:

• Black wins if it reaches the opposite side.
• White wins if it blocks black in such a way that black can not make any move anymore.
• Only diagonal moves (of length 1) on empty squares are allowed.
• White only moves forward.
• Black can move backward and forward.
• Black may make the first move, then white makes a move, and so on...

A street of length L is randomly filled with cars (one by one), where the length of a car is the unity of L (i.e. 1).