<h3>
The number of cards in the deck now is 47.</h3>
Step-by-step explanation:
Let us assume there are a total of m cards and m< 52.
If cards are divided by 4 the number of cards are left undivided = 3
⇒ 4 K + 3 = m ( K : Card given to each player)
So, minimum value of m can be 7
Possible values of m = {7,11,15,....,35,39,43, 47,51} ... (1)
As they all leave 3 cards when divided into 4 people equally.
If cards are divided by 3 the number of cards are left undivided = 2
⇒ 3 S + 2 = m ( S : Card given to each player)
So, minimum value of m can be 5.
Possible values of m = {5,8,11,....,38,41,44, 47,50} ... (2)
As they all leave 2 cards when divided into 3 people equally.
If cards are divided by 5 the number of cards are left undivided = 2
⇒ 5 L + 2 = m ( L : Card given to each player)
So, minimum value of m can be 7.
Possible values of m = {7,12,17,....,37,42, 47} ... (3)
As they all leave 2 cards when divided into 5 people equally.
Now, as we can see in all the three sets, the value of <u>m = 47 is in common in all sets</u>.
Hence, the number of cards in the deck now is 47.
