What is it?

Sun.

What is it?

Sun.

SWIMS.

14 + 13 = 7

11 + 15 = 6

17 + 18 = ?

15

31

what is x+y+z=?

X+Y=10

Y=10-X Use this to substitute for Y

X+Z=20

Z=20-X Use this to substitute for Z.

Y+Z=24 Substitute for Y and Z

(10-X)+(20-X)=24

30-2X=24

-2X=-6

X=3

X+Y=10 Put in value for X.

3+Y=10

Y=7

X+Z=20 Plug in value for X.

3+Z=20

Z=17

CHECK:

Y+Z=24

7+17=24

24=24

X+Y+Z=?

3+7+17=?

27=?

ANSWER: The sum X+Y+Z=27

We will be using the concept of LCM(Least Common Multiple) to solve this.

We know that the smallest 4-digit number is 1000.

LCM of 18, 24 and 32 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.

Thus, we have 288 as the smallest number, which is exactly divisible by 18, 24, and 32.

Since it's not a 4-digit number, we need to find the multiple of 288, close to 1000.

Here we have 136 as the remainder.

Therefore, we need to subtract 136 and add 288 to make the smallest 4 digit number exactly divisible by18, 24, and 32.

So, the multiple of 288 just above 1000 is: 1000 – 136 + 288 = 1152.

Hence, the smallest 4-digit number which is divisible by 18, 24, and 32 is 1152.

as delicated as ther morning dew;

as angel's dusting from the stars,

that can turn the Earth into a frosted moon.

What I am?

Bow.

How long does it take to fill the water-cask with the three taps together?

Together they fill 1/20 + 1/12 + 1/5 = 1/3 water-cask in 1 minute. Therefore, the whole water-cask is filled in 3 minutes.

What is the largest number of bitterballs that cannot be ordered in these portions?

Every natural number is member of one of the following six series:

0, 6, 12, 18, ...

1, 7, 13, 19, ...

2, 8, 14, 20, ...

3, 9, 15, 21, ...

4, 10, 16, 22, ...

5, 11, 17, 23, ...

If for a number in one of these series holds that it can be made using the numbers 6, 9, and 20, then this also holds for all subsequent numbers in the series (by adding a multiple of 6).

To find out what the largest number is that cannot be made using the numbers 6, 9, and 20, we therefore only need to know, for every series, what the smallest number is that can be made in that way.

In the series 0, 6, 12, 18, ... the smallest number that can be made is 0, so there is no number that cannot be made.

In the series 1, 7, 13, 19, ... the smallest number that can be made is 49 (20+20+9), so 43 is the largest number that cannot be made.

In the series 2, 8, 14, 20, ... the smallest number that can be made is 20, so 14 is the largest number that cannot be made.

In the series 3, 9, 15, 21, ... the smallest number that can be made is 9, so 3 is the largest number that cannot be made.

In the series 4, 10, 16, 22, ... the smallest number that can be made is 40 (20+20), so 34 is the largest number that cannot be made.

In the series 5, 11, 17, 23, ... the smallest number that can be made is 29 (20+9), so 23 is the largest number that cannot be made.

What is the length of the railway-bridge?

Let the length of the bridge be x meters.

Running towards the train, Charles covers 0.5x-10 meters in the time that the train travels x-4 meters. Running away from the train, Charles covers 0.5x+2 meters in the time that the train travels 2x-8 meters.

Because their speeds are constant, the following holds:

(0.5x-10) / (x-4) = (0.5x+2) / (2x-8)

which can be rewritten to

0.5x^2 - 24x + 88 = 0

Using the quadratic formula we find that x=44, so the railway-bridge has a length of 44 meters.

Which numbers are these?

Factorize the number 10000: 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5. Neither of the two numbers can contain the combination 2 × 5, because then the last digit of the number is definitely a zero. So one number has to be 2 × 2 × 2 × 2 = 16 and the other number 5 × 5 × 5 × 5 = 625.

What is the total number of toes in the bus?

The puppies: 4 children × 4 backpacks × 4 dogs × 4 puppies × 4 legs × 4 toes = 4096

Plus the dogs: 4 children × 4 backpacks × 4 dogs × 4 legs × 4 toes = 1024

Plus the children: 4 children × 2 legs × 5 toes = 40

Plus the driver of the school bus: 2 legs × 5 toes = 10

------- +

This gives the following total number of toes: 5170