To practice his counting, my grandson invented a card game he calls “Facetime”. He takes 2 decks of 54 cards (including the jokers) and lays them all out on the floor in a line, face up, mentally numbering them (1, 2, 3, etc., up to number 108). He then turns every other card face down, all the way down the line (so, all the even-numbered cards are face down). Next he looks at every third card and toggles it: if it’s face down, he turns it face up, and vice versa, all the way down the line. He then toggles every fourth card, and then every fifth. He continues this way, counting by every number (by 6’s, then by 7’s, etc.) until he has finished counting by 108’s (which doesn’t take long, since that’s how many cards there are.) When he’s done, which cards are lying face up
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
To practice his counting, my grandson invented a card game he calls “Facetime”. He takes 2 decks of
54 cards (including the jokers) and lays them all out on the floor in a line, face up, mentally numbering
them (1, 2, 3, etc., up to number 108). He then turns every other card face down, all the way down the
line (so, all the even-numbered cards are face down). Next he looks at every third card and toggles it: if
it’s face down, he turns it face up, and vice versa, all the way down the line. He then toggles every fourth
card, and then every fifth. He continues this way, counting by every number (by 6’s, then by 7’s, etc.)
until he has finished counting by 108’s (which doesn’t take long, since that’s how many cards there are.)
When he’s done, which cards are lying face up
Since on every turn, the card's position is changed. Therefore, the card number which has an even number of divisors (other than 1) will be faced up and the numbers which have an odd number of divisors (other than 1) will be faced down.
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