Page 38 - NUMINO Challenge_C2

Basic Concepts Applications of Parity

The chart below shows the shapes of each item as it is flipped over.

Number of

Side Flips Start 1 2 3 4

Showing

Card

Coin

Cup

When an object is flipped an odd number of times, the opposite side shows.
When it is flipped an even number of times, the starting side shows. Parity
reduces the trial and error process of complicated problems.

Example There are three cards all face up. The cards were flipped one at a
time, a total of 17 times. The 1st card is face down and the 2nd card
is face up. Is the 3rd card face up or face down? (Note that the
number of times each card was flipped is not known.)

Class Notes

The chart below shows the side that is showing when a card is flipped several times.

Number of Flips Start 1 2 3 4 5

Side Side Back Front
Showing

When a card is flipped an odd number of times, the (front, back) shows, and when a card is
flipped an even number of times, the (front, back) shows.

The 1st card is showing the back; therefore, it was flipped an (even, odd) number of
times. The 2nd card is showing the front; therefore, it was flipped an (even, odd) number
of times.

The three cards were flipped 17 times. The last card was flipped an (even, odd) number of
times. Therefore, the side that is showing is the (front, back).

35Words and Logic