TIMO THPT – Vòng Quốc gia (Heat Round) – Đề số 3

Find the number of positive integers less than 500, with unit digit 7 and has an even number of factors. number:

Số chẵn;

Positive integer: Số nguyên dương; Less than: Nhỏ hơn; Unit digit: Chữ số hàng đơn vị; Even

Factor: Ước

There are 34 marbles. A and B take marble alternately. Starting from A, each player can take 1,2 or 3 marble(s) and then pass to the other player. If the player who takes the last marble wins the game, and A takes 3 marble first, how many marble(s) should B take in his first move to ensure he will win the game?

Alternately: Luân phiên; Ensure: Chắc chắn.

36 children, numbered 1 to 36, sit around a circle in clockwise order. Starting from 1 and counting clockwise, the third child is selected and leaves the circle. Then the process starts repeating from the child on the next to the child just left the circle, the third child is selected and leaves the circle. For the process to continue, what is the number of the last child who remains in the circle?

đồng hồ;

Numbered: Được đánh số; Sit around a circle: Ngồi thành vòng tròn; Clockwise: Theo chiều kim

Third child: Người thứ ba

The next to: Kế tiếp