Page 37 - NUMINO Challenge_C2

4 Parity Strategies

Basic Concepts Parity

Even and odd numbers have the following characteristics.

(Even) (Even) (Even) (Even) (Odd) (Odd) (Odd) (Odd) (Even)

(Even) (Even) (Even) (Even) (Odd) (Odd) (Odd) (Odd) (Even)

(Even) (Even) (Even) (Even) (Odd) (Even) (Odd) (Odd) (Odd)

(Odd) (Odd) (Odd) (Odd) (Odd) (Odd) (Odd) (Even)
(Odd)
(Even)

The sum of two consecutive integers is always odd.

If the sum of two numbers is even, the difference is also even. If the sum

of two number is odd, the difference is also odd. Solving complicated

problems using these characteristics of even and odd numbers is called

parity.

Example Is the result of each calculations even or odd?

123 99 100

50 49 48 47 46 45 321

Class Notes

In , there are 50 even numbers and 50 odd numbers in 1 2 3 99 100.

The sum of 50 even numbers is an even number, and the sum of 50 odd numbers is an
odd number. Therefore, the result is (even, odd).

In , there are 25 consecutive number pairs. Therefore, there are 25 even numbers and
25 odd numbers.

The sum of 25 even numbers is even and the difference of 25 odd numbers is odd.
Therefore, the result is (even, odd).

Try It Again In the numbers from 1 to 100, is the difference between the
sum of all the even numbers and the sum of all the odd
numbers, even or odd?

34 NUMINO Challenge C2