TIMO 2018 Grade 3 Heat Set 4

What is the value of the number to represent “?” in the following table?

| First | Second | Third |
|---:|---:|---:|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | ? |

According to the pattern shown below, how many circle(s) is / are there from the 1st to the 165th symbol counting from the left? ○ △ □ ○ ○ △ △ □ □ ○ ○ ○ △ △ △ □ □ □…

The age of Samuel 6 years later is equal to the age of Joseph 4 years ago. Given that Samuel is 12 years old now, how old is Joseph now?

John wrote a 3-digit number on a piece of paper and asked Peter to guess it. Peter asked: “Is the number 189?” John replied: “One of the digits is correct. The position of that digit is correct.” Peter asked again: “Is the number 172?” John replied: “One of the digits is correct. The position of that digit is wrong.” Peter asked again: “Is the number 975?” John said: “One of the digits is correct. The position of that digit is also correct.” Given all the digits in that 3-digit number are different, find the number written by John?

According to the pattern shown below, how many ⊗ are there in the 10th Group?

Find the value of: $1+2+3$+...+$18+19+20$.

Find the value of 25×$12+75$×$21+25$×25.

Find the value of 1221×121.

Find the value of $123+234+345+456+567+678+789+890+901$.

Find the value of 2×4×8×16×5×25×125.

Define the operation symbol a⊕b=a×b+a÷3, find the value of (12⊕21).

The sum of A and B is 2017. The difference between A and B is 1221. Given A is larger than B, find the value of A.

Find the sum of the 15th term and the 16th term in the arithmetic sequence below. 21, 33, 45, 57, 69, ...

The sum of A and B is 1221. A is 10 times of B. Find the value of A.

What is the smallest 3-digit number that can be divisible by 3 and 5?

How many square(s) is / are there in the figure below?

A pyramid has 2017 faces, how many vertice(s) does this pyramid have?

At most how many right angle(s) could a pentagon (5-sided polygon) contain?

At least how many square(s) can be seen if observing the figure from the right-hand side?

At most how many triangles are formed by drawing 5 straight lines on a plane?