# Math Brain Teasers Page 1

# Simple Math

What number is one half of one quarter of one tenth of 400?

# Train Meeting

1 train leaves from NYC heading towards LA at 100 mph. Three hours later, a train leaves from LA heading towards NYC at 200 MPH. Assume there's exactly 2000 miles between LA and NYC. When they meet, which train is closer to NYC?

# Simple Math 1

What number is two-thirds of one-half of one-fourth of 240?

# Simple Math 2

Which is greater - half of quarter or quarter of half?

# Smoking Bum

As they say, beggars can't be choosers, in fact bums take what they can get. A bum on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the bum finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

# 3 Balls in a Box

Four blindfolded girls were each given an identical box, containing different colored balls. One contained 3 black balls; one contained 2 black balls and 1 white ball; one contained 1 black ball and 2 white balls; and the fourth contained 3 white balls.

Each box had a label on it reading "Three Black" or "Two Black, One White" or "One Black, Two White" or "Three White." The girls were told that none of the four labels correctly discribed the contents of the box to which it was attached. Each girl was told, in turn, to draw 2 balls from her box, at which point her blindfold was removed so that she could see the 2 balls in her hand and the label on the box assigned to her. She was given the task of trying to guess the color of the ball remaining in her box.

As each girl drew balls from her box, their colors were announced for all the girls to hear; but the girls cold not see the labels on any other box other than their own. The first girl, having drawn 2 black balls, announced: "I know the color of the third ball." The second girl drew 1 white and 1 black ball, and similarly stated: "I know the color of the third ball." The third girl withdrew 2 white balls, looked at her label, and said: "I can't tell the color of the third ball." Finally, the fourth girl declared: " I don't need to remove my blindfold or any balls from my box, and yet I know the color of all three. What's more, I know the color of the third ball in each of your boxes as well." The first three girls were amazed by the fourth girl's assertion and promptly challenged her. She proceeded to indentify the contents of each box correctly. How?

# Management Vs. Labor

A company gives a choice to two plans to the union negotiator for an increase in salary. The first option is an initial salary of $20,000 to be increased after 12 months by $500. The second option is an initial salary of $20,000 to be increased after each six months by $125. The salary is to be calculated every six months. Can you advise the union negotiator which is the plan he should recommend to his members?

# Father and Daughter

I am four times as old as my daughter. In 20yrs time I shall be twice as old as her. How old are we today?

# Calculator

Assume you are using a basic calculator and press the numbers in the order shown, using each of the symbols +, -, x, /, once only in this sum, what is the highest whole number possible ?

4 ? 1 ? 9 ? 8 ? 7 = ?

# Dart Board

A special dartboard has only eight segments. The segments are numbered clockwise from the top as follows:

15, 3, 6, 4, 12, 5, 10, 0

The number on each segment corresponds with its unique point score. How many different combinations are there to score 18 on this dartboard using three darts only ? Each dart lands in a segment and no dart falls to the floor.

# Caterpillar in the Garden

A caterpillar crawls at a speed of 21 inches per hour towards a vegetable patch. After being overindulgent it returns, over exactly the same distance, at only 7 inches per hour. What is the caterpiller's average speed over the entire journey ?

Note: The "journey" does not include over indulging in the vegetable patch.

# Check's in the Mail

A man received a check in the mail. The pounds had been transposed for pence and vice versa. He went out, spent 5 pounds and 42 pence but discovered that he now had exactly six times the value of the correct check. What amount should he have received?

# Calculator 2

Assume you are using a basic calculator and replace each question mark with a mathematical sign. Plus, minus, multiply and divide can each be used once only.

3 ? 7 ? 5 ? 4 ? 3 = ?

What are the highest and lowest possible totals ?

# Paper Cups

A recycling factory makes its own paper cups for canteen use. It can make one new cup from nine used ones. If it has 505 used cups how many can it possibly make in total ?

# Fruit Market

One satsuma, one apple and two pears cost 51p. Two pears and two satsumas cost 42p and one apple, one pear and two satsumas cost 44p.

How much will two apples and two satsumas cost ?

# De-Sync

Two clocks were correct at midnight but then one began to gain four minutes every hour. It stopped one and a half hours ago showing 4:48 pm. The clocks run for less than 24 hours.

What time will the other clock be showing ?

# Safe Harbor

A ship is battling against the tide to safety. It uses 9.5 gallons of fuel every hour and sails at 23 mph. It is 34 miles from safety but the flow against it is 12 mph. It has 30 gallons of fuel left.

Will it reach safety ?

# Party Ice

You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won't get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. What's the fastest way to make 120 full-sized ice cubes?

# Back From the Store

If you drive to the store at 20 mph, how fast must you go (again returning by the same route) for your average speed to be 40 mph?

# 15 in a Row

Arrange the numbers 1 through 9 on a tic tac toe board such that the numbers in each row, column, and diagonal add up to 15.

# The Bird and The Trains

Two trains travel toward each other on the same track, beginning 100 miles apart. One train travels at 40 miles per hour; the other travels at 60 miles an hour. A bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. When it reaches the slower train, it turns around, flying the other direction at the same speed. When it reaches the faster train again, it turns around -- and so on. When the trains collide, how far will the bird have flown?

# Elevator Crash

Suppose you are on an elevator on the 16th floor of a building, when the cable breaks. As you plummet toward the ground, you recall that you once heard that by jumping up FAST at the instant of impact, you can escape death. You also recall that the floors are twelve feet apart and that the speed of a falling object is 32 feet per second squared. When should you jump?

# Dog Run

A dog can run fifty miles in a day. How far could he run into a 120 square mile forest in two days?

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