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SOML MEET EVENT 3 Number Sense 1. NAME: _____________ TEAM: _____________ SCHOOL: _____________ [2 Points] You add together 57 numbers and the sum is even. What is the least amount of odd numbers used so the sum is even? What is the greatest amount of odd numbers used so the sum is even? ANS: Least _____, Greatest _____ 2. [3 Points] The word “level” is a five letter palindrome – the letters read left-toright give the same word as if read right-to-left. How many five digit palindromes are there? [Note: do not count five number strings which begin with ‘0’.] ANS: _________ 3. [5 Points] Consider the number 8 99 . What digit is in the 1’s place? ANS: _________ SOML MEET EVENT 3 Number Sense 1. NAME: _____________ TEAM: _____________ SCHOOL: _____________ [2 Points] You add together 57 numbers and the sum is even. What is the least amount of odd numbers used so the sum is even? What is the greatest amount of odd numbers used so the sum is even? Solution: Least ___0___ ( The sum of any even numbers added together is even.) Greatest ___56___ (Only pairs of odd numbers can add to an even.) ANS: Least 0, Greatest 56 2. [3 Points] The word “level” is a five letter palindrome – the letters read left-toright give the same word as if read right-to-left. How many five digit palindromes are there? [Note: do not count five number strings which begin with ‘0’.] Solution: The first digit will have 9 choices (1-9), the second digit will have 10 choices (0-9), and the third digit will have 10 choices (0-9). The other two digits will be determined by the first two so they will not have any choices. 9 *10 *10 = 900 ANS: 900 palindromes 3. [5 Points] Solution: 8n 81 82 Consider the number 8 99 . What digit is in the 1’s place? RESULT 8 64 LAST DIGIT 8 8 × 8 = 64 *8 multiplied by any number ending in 8 will end in 4. 3 512 8 × 4 = 32 8 *8 multiplied by any number ending in 4 will end in 2. 4 4096 8 × 2 = 16 8 *8 multiplied by any number ending in 2 will end in 6 5 32,768 8 × 6 = 48 8 *8 multiplied by any number ending in 6 will end in 8. * * * * * * 99 * 2 8 Note the repeating pattern of the ending digits: 8,4,2,6,8,4,2,6 … As this pattern is repeated, you will find that the last digit of 8 99 is 2. ANS: 2