TIMO 2018 Grade 6 Heat Set 4

Given A and C are two non-zero digits, we have:
1. CA is divisible by 19;
2. AC can be expressed by a product of 2 prime numbers;
Find the 2-digit number CA .

5 numbers, A, B, C, D and E, represent different numbers from 1 to 9.
Given the following conditions:
1. The sum of A and E is less than the sum of C and 5.
2. The sum of A, C and E equals D.
3. The sum of A and D equals B.
4. D is divisible by C.
5. The sum of A and C is less than E.
6. D is greater than 6.
Find the number to represent C.

20 children, numbered 1 to 20, sit around a circle in order. Each child has an integer in
hand. The child numbered 1 has the integer 1. The child numbered 2 has the integer 2.
The child numbered 3 has the integer 3. Given that the sum of the integers of any 8
consecutive children is equal to 20. What is the integer held by the child numbered 20?

John wrote a four-digit number with different digits. Peter guessed 1736: three digits are correct but all in wrong positions. He guessed 2345: two digits are correct but both in wrong positions. He guessed 3271: all four digits are correct but all in wrong positions. What number did John write?

There are 3 pieces of white chopsticks, 4 pieces of yellow chopsticks and 5 pieces of
brown chopsticks mixed together. If you want to get 2 pairs of chopsticks with different
colours in the dark, at least how many pieces of chopsticks should be taken out?

Find the value of 1+2+4+8+16+...+4096.

Find 1/(1×2)+1/(2×3)+...+1/(2016×2017).

Find the value of 1×2+2×3+3×4+...+99×100+100×101.

Find the value of 1+3+5+...+2015+2017+2015+...+5+3+1.

Convert 0.20171717... into the simplest fraction.

If 10-digit number A20171221B is divisible by 56, find the value of A + B .

Find the last digit of A if A=1²+2²+3²+...+2017².

2017 can be written as a product of 1221 positive integers. Find the sum of these 1221
numbers.

The remainder of dividing a positive integer K by 17 is 4. What is the remainder of
dividing (4K − 13) by 17?

Find the sum of all positive prime factor(s) of 1221.

How many rectangles are there in the figure below?

In the figure below, the area of rectangle ABCD is 200cm2. In the triangle HEB, the length
of base HE and altitude HI are 9 cm and 15cm respectively. Given that the sum
S ΔABF + SGBCD + S HEGF = 207.5 cm2. Find the area of the shaded region in cm2.

Small cubes with side length 1cm are combined according to the pattern shown below, if
there are 10 layers, find the volume.

A big rectangle is formed by 1221 squares with side length 1cm. Find the minimum
value of the perimeter in cm.

The figure below is a square with side length 14 overlapped by two quarter circles. Find
22
the perimeter of the shaded region. (Take π= ).
7