Problems that first-graders easily solve
You can achieve minimal time if there are always two pancakes in the pan. Then you can cook them all in six minutes.
Problems for the second grade
Who was the last minister, a knight or a knave?
Problems for the third grade
There are four possible outcomes: 1. The first assistant fell asleep; 2. The second assistant fell asleep; 3. Both assistants fell asleep; 4. Nobody fell asleep.
Problems for the fourth grade
The problem is equivalent to a system of comparisons X ≤ 350
2nd hint
Put the solution of the last comparison Х=8k+1, k=0,1,2… into the second one:
(8k+1)mod7=kmod7+1≡4, k=3⇒X=25+56m;
Then put it back into the first one.
Triangle ABD is the right triangle.
Problems that are easily solved by the fifth graders who study with Yakov Abramson
Angle ANB = angle AHB = angle B 1 HA 1, and angle CB 1 HA 1 is inscribed.
Based on the similarity of the corresponding pairs of triangles BA2 and OL2, CA4 and OL4, we formulate a system of equations.
Problems for the sixth graders
The total amount of time between two drives is 40 minutes, and the time when the car should leave the train station for the first time must be a multiple of 7.
Problems for the seventh grade
1st hint
Equation +x+2=X simulates this problem and is reduced to the form:
81х=2х² -72х+8×81
2nd hint
The problem implies that X must be an integer; it follows then that X must an even number and a multiple of 9: х=2*9k. After substitution, we see that k must be a multiplier of 4, k=4m.
Problems for the eighth grade
Angle ION is external to triangle AON, and AMIN is inscribed.
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A problem that students solve in the ninth grade
The director and his deputy meet only if |x-y| is greater or equal to 1. The probability of their meeting is equal to the ratio of the area of this strip to the area of the whole square.
The problem that is given in the freshman year at the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University and easily solved by tenth graders
The problem that is given in the sophomore year at the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University and easily solved by eleventh graders who study Abramson Math
FGHE and HCKD are inscribed, hence angle CKH=a, hence F, H, and K lie on the same line.
Learn how to solve complex and non-standard problems with Abramson Math
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