by Bill Graham

1. The Green Tomatoes Rock Band

The Green Tomatoes rock band has four members, Beatrice, Darlene, Gladys and Paula. They play the bass, drums, guitar and piano. No one plays an instrument that begins with the same letter as her first name. Beatrice rooms with the piano player. Paula and the drummer take ballet lessons together. Gladys plays the bass which she borrowed from Beatrice. Which instrument does each play?

Start by making a grid to represent the possibilities in the problem. Put a mark on the grid when a combination cannot be true and a different mark when you're sure it is true. Since none of them plays an instrument that starts with the same letter as her first name, put a mark (like a —) in the appropriate boxes. Gladys plays the bass, so put a mark (like a √) in that box. No one else can play the bass and Gladys can't play another instrument, so mark the other boxes in Gladys's row and column.

	Beatrice	Darlene	Gladys	Paula
bass	—	—	√	—
drums		—	—
guitar			—
piano			—	—

2. Professional Occupations

Meet Arthur, Ben and Charles, each of whom has two occupations from among the following: doctor, engineer, teacher, painter, writer and lawyer. No two men have the same occupation. Who does what?

a) The teacher and the writer went fishing with Arthur.
b) The doctor had lunch with the teacher.
c) The painter is related to the engineer.
d) The doctor hired the painter to paint his house.
e) Ben lives in the house next door to the writer.
f) Charles beat Ben and the painter at tennis.

3. The Grid

Using the numbers one through eight, arrange them in the grid shown so that no two consecutive numbers (like 1&2, or 7&6, etc.) are next to each other horizontally, vertically or diagonally.

4. Murder Most Foul

Mills has been found dead in the lounge of a most exclusive club in London, his sherry poisoned. Four men, seated on a sofa and two chairs, all facing the fireplace, are discussing the dastardly deed. One chair is on each side of the sofa (see diagram). Their names are Davis, Smythe, Barton and White. They are a writer, teacher, architect and barrister, not necessarily in that order.

a) The waiter pours a glass of whiskey for Barton and a beer for Smythe.
b) In the mirror over the fireplace, the writer sees the door close behind the waiter. He turns to speak to White seated next to him.
c) Neither Davis nor Smythe has any sisters.
d) The teacher doesn't drink.
e) Davis, who is sitting in one of the chairs, is the architect's brother-in-law.
f) The teacher is next to Davis on his left.

Suddenly a hand moves stealthily to put something in Barton's whiskey. It is the murderer! No one has left his seat and no one else is in the room. What is each man's profession, where is each sitting and who is the murderer?