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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(1) Number grid

Fill the number grid given below with numbers from 0 to 9 in such a way that the entire number in the grid should contain as many 0s as given in the box above 0, as many 1s as given in the box above 1 and so on.

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| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | | |

--------------------------------------------------------------------------

| | | | | | | | | | |

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

| | | | | | | | | | |

--------------------------------------------------------------------------

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(2) Two mistaken students

A teacher writes a whole number less than 50,000 on the blackboard. One student states that the number is a multiple of 2; a second student states the number is a multiple of 3; and s on until a twelfth student says that it is a multiple of 13. The teacher remarks that all except two of the students were right and, moreover, that the two who were wrong spoke one after the other.

What was the number that the teacher wrote on the blackboard?

Character is who you are when no one is looking.

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

justlookingforthemoment,

the puzzle is to put a number in the grid such that the number os times the number appearing above 0 or 1 in the number should be indicated by

that number.

For example,

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| | | | | | | | | | |

| a | b | c | d | e | f | g | h | i | j |

| | | | | | | | | | |

--------------------------------------------------------------------------

| | | | | | | | | | |

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

| | | | | | | | | | |

--------------------------------------------------------------------------

if abcdefghi is the number, the number should contain a zeros, b ones, c twos, d threes and so on. There is no limit on the numbers to be used other than that the answer is a ten digit number and should satisfy the condition stated.

Character is who you are when no one is looking.

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

Oh, okay. I thought it was the number of times each digit appeared in the whole grid. But it is only meant to be counting the digits in the top number (is that right?).

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

*Last edited by ashwil (2006-03-11 02:50:12)*

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

Sorry, posted wrong answer to (2)! Try again!!

*Last edited by ashwil (2006-03-11 03:08:06)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

**The answer to (1) is correct, ashwil! Excellent! **

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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(3) You may use any mathematical sign such as +,-, x, ÷ and exponentiation (power). Get exactly 1,000 using

(a) five 9s

(b) six 9s

(c) seven 9s

(d) eight 9s and

(e) nine 9s.

Character is who you are when no one is looking.

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

3 (a)

*Last edited by ashwil (2006-03-11 03:46:32)*

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

3 (b)

*Last edited by ashwil (2006-03-11 03:46:57)*

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

Once 3(a) and 3(b) are answered, 3(c), (d), (e) are just extensions of the same principles

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(4) A little girl I know sells oranges from door to door. One day while on her rounds, she sold ½ an orange more than half her oranges to the first customer. To the second customer she sold ½ an orange more than half of the remainder and to the third and last customer, she sold ½ an orange more than half she now had, leaving her none.

Can you tell the number of oranges she originally had if she never had to cut an orange?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(5)The difference of the squares of two whole numbers is a cube and difference of their cubes is a square. Can you find the smallest pair of such numbers?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(6) Can you split the number 34 into two parts such that 4/7 of one part is equal to 2/5 of the other?

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

**Correct, mathsyperson! **

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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**(7) I asked the captain of a ship how old the ship was. He pointed to a boiler in the ship and said, "The ship is twice as old as the boiler was when the ship was as old as the boiler is now. The combined age of the ship and the boiler is thirty years."**

**Can you figure out the age of the ship and the boiler?**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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**(8) A man is 6 years older than his wife. Four years ago, he noticed that he had been married to her for half his lif.How old will the man be when he has been married for fifty years, if in ten years time,his wife would have been married to him for two-thirds of her life?**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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**(9) There are many factorials that can be expressed as the produce of two or more other factorials. For example, 7! x 6! = 10!. Can you think of any other?**

**(10) In the following multiplication, what single digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) should replace the '*'? 7451 x 3982 = 29*69882**

**(11) Only two rectangles have dimensions that are integers and their area and perimter are numerically equal. Can you find them both?**

**(12) Complete the series:**

**6, 24, 60, 120, 210, 336, ______**

**(13) Can you divide 1000 into two parts such that one part is a multiple of 47 and the other a multiple of 19? **

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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** (14) When Dr. Cohen finally finished typing her treatise, "The Sleeping Habits of Colombian Edible Ants", she was rather suprised to notice thatm the number of digits she used to number its pages was exactly a multiple of the number of pages in the treatise itself. This substantial piece of work contains over 1,000 pages, but fewer than 10,000. Exactly how many pages does it contain?**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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**(15) There are 100 marbles in five bags. If the first and second bags contain between them 52 marbles, the second and third together contain 43, the third and fourth contain 34, and the fourth and fifth contain 30 marbles, how many marbles are there in each bag?**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,256

(16) The * in the multplication represents a single digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or9). Can you tell the number without actual multiplication?

**1649 x 6313 = 10*10137 **

Character is who you are when no one is looking.

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