Solution:

Starting with 1 marble in a bag, each bag contains double the number of marbles as the previous bag.
ie 1,2,4,8,16,32,64,128,256,512.

That way whatever number of marbles I would ask for you would just add up the boxes to equal the number asked.

Solution:

1) 8/(3-(8/3))
= 8/(1/3)
= 24

2)((8 x 3!)/3)+8
= ((8 × 3 × 2 × 1)/3)+8
= (48/3)+8
= (16)+8
= 24

3)(3!/)*8

4)(8-3)!/(8-3)
( × )!
( + )!
?(8×8×3×3)
8+(8×(3!/3))
((?(8+8) × (3/3))!
?(8+8) × (3+3)
(log base(3!/3) of 8) × 8
((log base(3!/3) of (8+8))!

Solution:

Only Statements 1 and 3 are true. the number is 499849.

7072 = 499849
499849 < 500000

Solution:

10 miles
Speed us 10miles/hour

Solution:

The digits of the requested two numbers obviously form descending sequences. Furthermore, if you have two pairs of numbers with equal sums, the pair of which the numbers have the smallest absolute difference, is the one of which the numbers have the largest product. Using this knowledge, the two numbers can easily be constructed by placing the digits one by one, starting with 9 and ending with 1:<br>9<br><br>8 -> 96<br><br>87 -> 964<br><br>875 -> 9642<br><br>8753 -> 9642<br><br>87531<br>Conclusion: the requested two numbers are 9642 and 87531 (and the product of these two numbers is 843973902).

Solution:

The complete addition looks as follows:

  167161 +
  664711 +
  162166 +
  164611
-------------
1158649

Solution:

9376

Looking at the last digit, the last digit must be either 0, 1, 5 or 6.
Then looking at the last two digits, the last two digits must be either 00, 01, 25 or 76.
Then looking at the last three digits, the last three digits must be either 000, 001, 625 or 376.
Then looking at the last four digits, the last four digits must be either 0000, 0001, 0625 or 9376.
Out of those, only 9376 is a 4 digit number

Solution:

33 seconds

The train takes 30 seconds to travel 1 mile, plus 3 seconds for the complete train to pass any point, making a total of 33 seconds.

Solution:

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be 'changed' an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.

Solution:

There are 49 steps.

He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 pac