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Interesting mathematical Olympics
(1) If a number is followed by 6, the number is increased by 60000, and the number is (6666).

10x +6=x+60000, and x is obtained.

(2) It has an isosceles trapezoid with a base angle of 45 degrees, an upper base of 8 and a lower base of 12. The area of this trapezoid is 20.

Height (12-8)/2=2, area =(8+ 12)*2/2=20.

(3) When a number is divided by 1, it is1,and when it is divided by 18, it is 15. The minimum number is (34).

A number divided by 12 and 10, divided by 18 and 16, the smallest number is 12, and the least common multiple of 18 is 36 minus 2,36-3 = 34.

(4) It is known that a×b+ 13=x, where both a and b are prime numbers less than 1000 and x is odd, then the maximum value of x is (2*997+ 13=2007).

X is odd, one of A and B must be even, even prime number is 2, A = 2, and the largest prime number of B less than 1000 is 997.

⑤ Dice (cube). The sum of two opposites is 7. Put it on the table. Xiao Gang sees the front (1), the right (5) and the top (3), and the sum of the three numbers is 9. Xiao Qiang sees the back (6), the left (2) and the top (3), and the sum of the three numbers is 1 1. The number at the bottom is (4).

9 = 1+3+5, 1 1 = 2+3+6, 1 to 6, 5 to 2, the top must be 3, and the remaining 4 must be the bottom number.