Math Olympiad for 3rd Grade – 3

Posted on September 24, 2021 by kevin
  1. Black stones and white stones are arranged on the table in the following pattern: 
    ⚫◯◯⚫⚫⚫◯⚫⚫◯◯◯⚫◯◯⚫⚫⚫◯⚫⚫◯◯◯⚫◯◯⚫⚫⚫ ......
    The color of the 999th stone is __________ and there are ____________ white stones among the 999 stones.
  2. For the following sequence of numbers: $$1, 4, 7, 10, 13, 16, 19, 22, 25, …….$$ The $2020^{th}$ number in the above sequence is ________.
  3. For the following sequence of numbers: $$1, 2, 4, 7, 11, 16, 22, 29, ……$$ where the first number is $1$, the second number is one more than the first, the third number is one more than the second, and so on. The remainder of the $2020^{th}$ number divided by 5 is __________.
  4. Chaining the following sequence numbers together $$1, 2, 3, 4, …… 97, 98, 99, 100, 101$$ to form a very big number $$123456……979899100101$$ There are __________ digits in the above big number.
  5. The product of $10000$ natural numbers is $10000$. The maximum sum of those $10000$ numbers is __________.

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Math Olympiad for 3rd Grade – 2

Posted on September 17, 2021 by kevin
  1. The total number of 2-digit positive integers with the ten-digit greater than the unit-digit is __________.
  2. The sum of 20 consecutive natural numbers is 2010. The smallest one is __________ and the largest one is __________.
  3. The following are rows of equations: $$4+2=6$$ $$5+8=13$$ $$6+14=20$$ $$7+20=27$$$$……$$ The equation of the 99th row is __________.
  4. To cut a pizza into 11 pieces, the minimum number of straight cut required with a knife is __________.
  5. You are required to subtract 285 from 3000, add 282 to it; then subtract 285 and add 282 again; repeat the process until the number become 0. The number of subtractions performed is __________.
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Math Olympiad for 3rd Grade – 1

Posted on September 10, 2021 by kevin
  1. Use symbol $+$, $-$, $\times$ and $\div$ to fill in the blanks to make the following equation: $$ \texttt{1}\ \boxed{　}\ \texttt{2}\ \boxed{　}\ \texttt{3}\ \boxed{　}\ \texttt{4}\ \boxed{　}\ \texttt{5}\ =\ \texttt{20}$$
  2. Find the value of the following: $$9999999+999999+99999+9999+999+99+9$$
  3. Find the value of the following: $$1+2-3+4-5+6-7+8-9+…+2018-2019+2020$$
  4. Find the value of the following: $$1+2+3-4-5+6+7-8-9+…+2018+2019-2020$$
  5. $a$,$b$,$c$,and $d$ are different single digit numbers and $$ \begin{array} \ \ \ \ \ \ \ \ \texttt{ a b c d}\\ \ \ \ \dfrac{\times　　　\texttt{　　　9}}{　\texttt{ d c b a }}\end{array}$$ The value of 4-digit number $abcd$ is __________.
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Fun Math Puzzles – 1

Posted on August 17, 2021 by kevin

My calculator is broken, it only has two working buttons. One of them adds $1$ to the result and the other doubles it. What is the minimum number of presses needed to get to 2021?

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Geometry Challenge – 7 ⭐

Posted on August 4, 2021 by kevin

In parallegram $ABCD$, point $E$ and $F$ are on side $AB$ and $AD$ respectively. $EF$ intersects diagonal $AC$ at $G$. Show that $\dfrac{AB}{AE}+\dfrac{AD}{AF}=\dfrac{AC}{AG}$.

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