Instructions:
Simply click on the correct answer from the five
choices given.
Note – all of the contest number series have to do with number properties. What are number properties?
Examples:
Odd numbers 1,3,5,7, 9……
Even numbers 2,4,6,8,10……
Prime numbers 2,3,5,7,11…. (numbers whose only divisors are one and themselves).
Composite numbers 4,6,8,9,10, (numbers with more than two factors (divisors)).
Square numbers 1,4,9,16….
Cubes 1,8,27,64…..
Numbers with exactly four factors 6,8,10,14 (also called "near primes" – factors are divisors.)
Numbers divisible by five 5,10,15,20,etc.
Numbers whose remainder after division by five is one 1,6,11,16,21,….
Numbers whose sum of digits equals six 15,24,33,42,51….
Contest Problems From Prior Weeks
Last week’s problems and solutions.
1. The product of two perfect squares is never a square. True or False? Click here to try Problem 1 2. The product of an even number with an odd number is always ____. (even or odd) Click here to try Problem 2 3. In the number series 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, ... what number comes next? Hint - don't be a square! Click here to try Problem 3 4. The sum of two odd numbers will always be odd or even? 5. Can the product of two prime numbers ever be prime? 6. What is the only counting number that has a perfect square on one side and perfect cube on the other side? (Hard) 7. In the number series 11, 31, 71, 91, 32, 92, 13 ... What number comes next? Hint - think dyslexia.13. In the number series 11, 12, 14, 16, 20, 21, 23, 25 what number comes next?
14. In the number series 11, 14, 19, 22, 28, 33, 41, 44 what number comes next?
15. In the number series 1, 4, 0, 7, 7, 0, 4, 1, 0, 1 what number comes next? (hard)
17. Only one two-digit square number is the sum of two square numbers. Click here to try Problem 17 18. Only one two-digit square number has digits which themselves are square numbers.. Click here to try Problem 18 19. What is a two-digit square number that is the product of two unique square numbers greater than one? Click here to try Problem 19 20. What is a two-digit square number whose sum of digits is also a square number? Click here to try Problem 20 21. Only one two-digit square number is also a cube. Click here to try Problem 21 -------------------------------------------Cool number fact:
Prime numbers are the basis of secret codes! Because the Allied code breakers in WWII were able to solve the secret codes of Germany and Japan thousands of lives were spared. Math can save lives! The German code was broken by stealing the encrypting machine. The Japanese code was broken by the sheer brain power of the code breakers. Primes are the basis of current secret codes - it took the advent of the computer to find very large prime numbers.
--------------------------------------------