Mathematical Magic, Puzzles

One day in a shopping mall...

2008-08-17T10:39:00.000-07:00

A woman went to a shopping mall with a calculator. She is weak in calculation.

She took 4 items and calculate the total price by using calculator and got it as $7.11

She went to checkout queue. Unfortunately she multiply item's prices instead of sum those.

Counterman do the calculations properly (sum those) and charge the woman $ 7.11 (how strange!)

But that was true and none was mistaken.

Now what was the cost of each item she purchased?

The whole truth and nothing but the truth

2008-08-16T11:24:00.000-07:00

There is a island in the Pacific Ocean on which there are three tribe lives.

* the Whites, who always tell the truth,
* the Blacks, who always tell lies,
* and the Greys, who lie and tell the truth alternatively but their first answer may be either trusth or lie.

These natives always gather in groups of three, with one representative of each tribe in the broup.

A visitor to the island approaches such a group of three natives, and had the following conversation with the

first native.

* Are you the White, the Black, or the Grey?
** I am the Grey.

* And what about yout friend here?
** He is Black.

* So your other friend is the White?
** Of course.

Now, a question to you. Was the 'other friend' white? and if not, what was he?

Find the perfect square...

2008-08-16T09:50:00.000-07:00

Perfect Square
Perfect square is a number that has a rational number as its square root.

Examples
49 is a perfect square as 49=7².
The following are few more examples of perfect squares.
1, 4, 9, 16, 25, 36, 49, 1/9, 16/49,....

Now the Quiz begins..
Let A, B, and C are three perfect squares having integers as their square root,
and A=(B+C)/2

What is the smallest value for A ?

Mathematical Puzzle: Make 24

2008-08-11T07:56:00.000-07:00

This problem was suggested by Eva Börgens in 2002. Eva attended the 7th form of Augustinerschule Friedberg, then.

Solve a random Make 24 Puzzle

Get solution for specific Make 24 Puzzle

MAKE 24 is a simple game. Four figures in the range of the natural numbers 1 to 9 are chosen randomly. Your task is to combine them in order to obtain the result 24 - but you may only use the four basic arithmetical operations and brackets.

Example: 6, 3, 6, 4 are the four numbers given.
Then 6 · 6 - 4 · 3 = 24 (you may find other solutions).

Now try:

6, 8, 9, 9

1, 3, 4, 6

3, 3, 7, 7

No ploys! Not allowed are factorials, powers, roots etc. Furthermore, you must not combine two or three of the four numbers to a two- resp. three-digit number (e.g., with 1, 3, 4, 8 given, 38 - 14 = 24 is no correct solution).

Note: There are 495 different games, of which 404 are solvable. The game with the most solutions is 1,7,8,9 which has 15 solutions.