A craftsman is asked to manufacture three universal weights so that, using only these weights and a simple balancing scale, it will be possible to measure any mass of consequtive integer number of grams, starting from 1 gram, 2 grams, etc., up to a maximum possible mass of N grams. It is allowed to place any of the three weights in any of the sides of the balancing scale, or to put any of them aside. What is the greatest possible mass, N grams, that one can measure, given these requirements?

(A) 6g          (B) 7g          (C) 9g          (D) 10g          (E) 13g

What is 1 + 1 written in base 2?

Prove that:

\(x^2+2x+3⋮x+1\)

Find x:

\(\left(3-4x\right)^3=-125\)

Find x:

\(5^x+5^{x+1}=750\)

Express the power:

\(\dfrac{81^4.3^{10}.27^5:3^{12}}{3^{18}:9^3.243^2}\)

Because after Summer Clouds's warning, there is still many situations of violeting the rules. Here is the chart of the members violeted the rules:

Vũ Hà Vy Anh: 7 (Create an account and self-tick)

TOTAL: 18 from 7 accounts.

There are still 6 more members who break the rule but I only list more than 3 break-rules. I hope Summer Clouds would have a way to solve this problem. 

The digits 2, 0, 1 and 4 are used to create every possible positive four-digit integer, with each digit used exactly once in each integer. What is the arithmetic mean of all these integers?

How many elements are in the set {x\(^2\) − 2x + 1 | x = −5, −4, ... , 4, 5}?

In Bag A are 9 red balls and 1 green ball. A player gets one draw from Bag A and wins if the green ball is selected. In Bag B are 99 red balls and 1 green ball. A player gets 20 draws from Bag B and wins if the green ball is selected, but if the selected ball is red, it must be returned to the bag before the next draw. What is the absolute difference between the probability of winning with Bag A and the probability of winning with Bag B? Express your answer as a decimal to the nearest thousandth. 

An ice cream cone is 5 inches tall with a radius of 1.5 inches. The outer surface area of the cone is covered with chocolate. How many square inches of cone are covered with chocolate? Express your answer as a decimal to the nearest tenth.

The time, t seconds, that it takes for a rock to fall a distance, d meters, is approximately t = \(0,45\sqrt{d}\). How many seconds does it take a rock to fall 200 m? Express your answer as a decimal to the nearest tenth.

If RATS × 4 = STAR, and each letter represents a different digit from 0 to 9, inclusive, what is the value of S + T + A + R?

The first three terms of an arithmetic sequence are p, 6 and 2p – 3. What is the tenth term of this sequence?

The six integers 1, 3, 5, 7, 9 and 11 form an arithmetic sequence. If three of the integers are selected randomly without replacement, what is the probability that they form an arithmetic sequence in the order they are selected? Express your answer as a common fraction.

If \(\dfrac{64^8}{32^{-3}}=2k\) then what is the value of k ?

What is the units digit of \(1!+2!+3!+...+2014!\)?

Vincent is building a structure out of LEGO® bricks. The top level (first level) is a rectangle of 1 brick by 2 bricks. The level directly below the top level (second level) is a rectangle of 2 bricks by 3 bricks. The third level is a 3-by-4 rectangle. If the pattern continues, how many bricks are needed to build a structure 12 levels high? 

What is the value of 1 − 5 ∙ 2 + 10 ∙ 2\(^2\) − 10 ∙ 2\(^3\) + 5 ∙ 2\(^4\) − 2\(^5\) ?

Silas has a clock that gains 15 minutes each hour; for instance, if it shows the correct time at 2:00 p.m., one hour later it will show a time of 3:15 p.m. when it should show 3:00 p.m. Last night, Silas set the clock to the correct time at 10:00 p.m. While he was sleeping, the clock stopped working, and it showed a time of 4:00 a.m. That was 4 hours before he woke up. At what time did Silas wake up?