Download 2005-2006 Meet 1

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