(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?

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,
--------------------------------------------------------------------------
    |         |         |        |         |         |         |        |         |         |         |
    |    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.

Last edited by ashwil (2006-03-12 01:50:12)

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

3 (b)

Last edited by ashwil (2006-03-12 02:46:57)

(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?

(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?

(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?

(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?