Algebra
If a number increases by 25% and becomes 125, what was the original number?
100
What is the name of a ray that originates from the vertex of an angle and divides it into two equal angles?
Bisector
The largest digit
9
2, 6, 18, 54, х,...
Х-?
X=162
A farmer needs to transport a wolf, a goat, and a cabbage across a river. He has a boat that can only carry him and one passenger. The wolf cannot be left alone with the goat, otherwise, it will eat it, and the goat cannot be left alone with the cabbage. How can the farmer transport everyone?
First, the farmer takes the goat across and leaves it on the other side.
He then goes back alone and takes the wolf across.
On the other side, he leaves the wolf and takes the goat back with him.
Next, he takes the cabbage across and leaves it with the wolf.
Finally, he returns for the goat and brings it across.Now, all three— the wolf, the goat, and the cabbage—are safely on the other side!
Find the least common multiple (LCM) of the numbers 36 and 48.
144
A twelve-sided polygon in other words
How many variants of exam tickets with two questions can be created from a list of 20 questions?
190
1, 4, 27 ,256 ,...
an=nn
On an island, there are knights who always tell the truth and liars who always lie.You meet two islanders, A and B. A says, "We are both liars." Meanwhile, B remains silent. Who is who?
"A" cannot be a knight because a knight would never say that he is a liar. Therefore, A is a liar.If A is a liar, then his statement "We are both liars" is false. This means that B must be a knight.
Find the sum of all numbers from 1 to 50.
1275
Which Greek mathematician of the 3rd century wrote Elements of Geometry?
Euclid
1+2+3+......+88=
3916
a1=3
d=4
S5=?
S5= 35
There are 81 balls.One of them has a different weight (it may be either lighter or heavier). You only have a scale, but it only shows the difference in weight between the two pans. How can you minimize the number of weighings to find the anomalous ball?
Divide the balls into 3 groups of 27. Weigh two of them. If the weights are equal, the defective ball is in the third group.Divide the remaining 27 balls into 3 groups of 9. Repeat the process.Repeat the steps with groups of 3, then with the 1 anomalous ball.
How many two-digit numbers exist where the tens digit is less than the ones digit?
36
What is the name of a geometric figure consisting of a point and two rays originating from that point?
Angle
Dr. Ai extracts a patient's tooth in 10 minutes, while.Dr. Oy does it in 6 minutes.
Dr. Ai applies a cast in 13 minutes, while Dr. Oy also does it in 6 minutes.Dr. Ai fills out insurance documents in 14 minutes, while Dr. Oy does it in 7 minutes.How much time will Dr. Ai and Dr. Oy spend on the patient if they work together and need to extract the tooth, apply the cast, and fill out the documents?
12
0, 1, 1, 2, 3, 5, 8, 13, ...
Sequence formula
Xn+2 = Xn+1 + Xn X1 = X2 = 1
100 prisoners stand in a row, each wearing either a black or a white hat. Each prisoner can see the hats of everyone in front of them but not their own.The prisoners must take turns naming the color of their own hat (starting from the last one in the row), and they cannot break the order. If they guess correctly, they survive; if not, they die.They can agree on a strategy in advance. How can they save the maximum number of prisoners?
The last prisoner counts the number of black hats he sees. If the number is even, he says "black"; if it is odd, he says "white."The rest of the prisoners remember his word as a key to parity: if their own count of black hats matches the parity of the word, their hat is white; if it does not match, their hat is black.Thus, the first prisoner may die, but all the others will guess correctly.
There are 100 people in a room, each with either a red or a blue dot on their forehead.
Everyone can see the dots on others but not their own.
The host announces: "There is at least one red dot."
If a person is certain of their own dot's color, they must leave the room.
After 100 seconds, all people with red dots left.
How many red dots were there?
There were 100 red dots.
What is the exact shape of the Earth?
Geoid
In the classroom, a certain four-digit number was written on the board. Two students entered the classroom and thought it was an example of multiplication of two numbers. One of them multiplied two two-digit numbers, while the other multiplied a single digit and a three-digit number. (For example, if 2345 was written, one could multiply 23 by 45, while the other could multiply 2 by 345 or 234 by 5.)The students obtained the numbers 845 and 3078.What was the original number written on the board? If there are multiple suitable numbers, write them in ascending order without spaces. If no such number exists, write 0 as the answer.
6513
5, 15, 45, 135,...
Sequence formula
an=5⋅3n-1
Student Mathematical Association