which number replaces the question mark?
30
Explanation:
As you can see the lower number rows are always bigger than upper row ones with the difference going up by 3 with every step
34 - 32 = 2
32 - 27 = 5 (difference going up by 3 from last difference)
56 - 48 = 8 (difference going up by 3 from last difference)
? - 19 = 11 (difference going up by 3 from last difference)
so ? = 30
If 21 is added to four times a number, the result is 57.
Then the number is?
9
4x + 21 = 57
4x = 36
x = 9
A fireman Jacob stood at the center of a ladder and was spraying water on a burning house.
He climbed up 6 rungs before the heat of the flames forced him to come down 10 rungs.
Some minutes later, Jacob climb 18 rungs to the very top of the ladder.
How many rungs did the ladder have?
29
Jacob standing on the middle rung.
He goes up 6 rungs so he is now at M+6 and when he goes down 10 rungs so he is at M-4.
Jacob goes up 18 rungs so he is now at M+14 = T
14 rungs from the top, 14 rungs from the bottom, and the middle rung. 14+14+1=29
What is the probability of rolling a sum of 7 with two fair six-sided dice?
0.1667 or 16.67%
When rolling two fair six-sided dice, there are a total of 36 possible outcomes (6 outcomes for the first die multiplied by 6 outcomes for the second die).
To calculate the probability of rolling a sum of 7, we need to determine the number of combinations that result in a sum of 7. These combinations are:
1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1
So, there are 6 favorable outcomes that result in a sum of 7.
The probability of rolling a sum of 7 is calculated by dividing the number of favorable outcomes by the total possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Possible Outcomes) = 6 / 36 = 1/6 ≈ 0.1667
Therefore, the probability of rolling a sum of 7 with two fair six-sided dice is approximately 0.1667 or 16.67%.
salman's youth lasted one sixth of his life. He grew a beard after one twelfth more. After one seventh more of his life, he married. 5 years later, he and his wife had a son. The son lived exactly one half as long as his father, and salman died four years after his son.
How many years did salman live?
The riddle, the 'facts' of which may or may not be true, results in the following equation:
x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
where x is salman's age at the time of his death.
Therefore, salmna lived exactly 84 years.
The Puzzle: Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight 'dots' .4.5.6.7.8.9.0. which would add up to 82
The dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc)
With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc)
The remarkable feature being that a proper fraction divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.
Charles walks over a railway-bridge. At the moment that he is just ten meters away from the middle of the bridge, he hears a train coming from behind. At that moment, the train, which travels at a speed of 90 km/h, is exactly as far away from the bridge as the bridge measures in length. Without hesitation, Charles rushes straight towards the train to get off the bridge. In this way, he misses the train by just four meters! If Charles would, however, have rushed exactly as fast in the other direction, the train would have hit him eight meters before the end of the bridge.
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
0.5x2 - 24x + 88 = 0
Using the abc formula we find that x=44, so the railway-bridge has a length of 44 meters.
Try to find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times
The number is: 12345679
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
And so on...
Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.
How many miles does the pigeon travel?
54
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles
A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps are there?
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