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UIL Number Sense & Math
Special Session
Larry White
Box 25
Millersview, Tx 76862
325-483-5446
[email protected]
UIL State Number Sense Contest Director
UIL State Mathemaics Contest Director
Be sure to ...
  sign in;
  fill out an information
sheet;
  clean up your area when
you leave;
  and
“HAVE A GREAT
DAY”
Special Problem #1
Find the sum of the positive
integral divisors of 24.
Solution 1:
1)  Prime factor 24:
2 x 2 x 2 x 3 = 2^3 x 3^1
2)  If exponent is 1, then add one to the number: 3 + 1 = 4
3)  (i) Add 1 to each exponent greater than 1: 2^4 = 16
(ii) Subtract 1: 16 – 1 = 15
(iii) Divide by the prime factor less 1: 15/(2-1) = 15
4) Multiply results: 4 x 15 = 60
Special Problem #1
Find the sum of the positive
integral divisors of 24.
Solution 2:
1)  Prime factor 24:
2 x 2 x 2 x 3 = 2^3 x 3^1
2)  Sum: 2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1 = 15
3)  Sum: 3^1 + 3^0 = 3 + 1 = 4
4) Multiply results: 4 x 15 = 60
Special Problem #1 (again)
Find the sum of the positive
integral divisors of 72.
Solution 1:
1)  Prime factor 72:
2^3 x 3^2
2)  (i) Add 1 to each exponent greater than 1:
2^4 = 16 and 3^3 = 27
(ii) Subtract 1: 16 – 1 = 15 and 27 – 1 = 26
(iii) Divide by the prime factor less 1:
15/(2-1) = 15 and 26/(3-1) = 13
3) Multiply results: 15 x 13 = 195
Special Problem #1 (again)
Find the sum of the positive
integral divisors of 72.
Solution 2:
1)  Prime factor 72:
2^3 x 3^2
2)  Sum: 2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1 = 15
3)  Sum: 3^2 + 3^1 + 3^0 = 9 + 3 + 1 = 13
4) Multiply results: 15 x 13 = 195
Special Problem #2
How many solutions are there for the
equation 2x + 5y = 70 such that both x
and y are positive integers?
UIL Mathematics Contest
Special topics/problems/ emphasis on
2012-2013 tests
No new mathematicians added this year.
No new special numbers added this year.
Emphasis this year on:
Platonic Solids
Pascal’s Triangle
Binomial Theorem
(note: see back of SAC test)
“INTERESTING” Numbers
1809
2010
6432
interesting
if the number formed by the leftmost two
digits is twice as large as the number formed
by the rightmost two digits. All interesting
numbers are divisible by a unique number d.
d = ???
A four digit number is considered to be
What are the first two interesting
numbers?
1005
1206
UIL
NUMBER SENSE & MATH
Questions & Answers
HAVE A
GREAT DAY!