Homework Statement
In how many ways can 68068 be written as the difference of two squares?Homework EquationsThe Attempt at a Solution
Let (x+a) * (x+a) -x*x =68068=2*2*7*11*13*17
a (2x+a) =2*2*7*11*13*17
As 2x+a is odd ⇒ a is even
∴a=2b
2b (2x+2b) =2*2*7*11*13*17
b (x+b) =7*11*13*17
x=...
Let us take suits as A, B, C, D
Now the different case which arises are
3 A 1 B 1 C 1D
1 A 3 B 1 C 1D
1 A 1 B 3C 1D
1 A 1 B 1C, 3 D
2 A 2 B 1C, 1D
2 A 1 B 2C 1D
2 A 1 B 1C 2 D
1 A 2 B 2C 1D
1 A 2 B 1C 2 D
1 A 1 B 2C 2 D
Therefore required number of ways will be 13*13*13 (4* 13c3) + 13*13*6...
Homework Statement
In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?Homework EquationsThe Attempt at a Solution
4 different cards can be chosen in 13*13*13*13 ways. Now we have to choose 2 remaining cards from 48 cards. This can be done in...
Yes, if d=0 is considered, nine more numbers are added to the solution set (1111 , 2222..., 9999)
However, my question is, a series (x, x, x, x, x, x, x) be considered an AP (that is can an AP have common difference=0)
Homework Statement
Of a 4 digit positive integer, the four digits form an Arithmetic progression from left to right. How many such 4 digit integers exist?
2. The attempt at a solution
If d = 1, the integers are 1234, 2345, …, 6789. These 6 integers and their reverses satisfy the given...
Mod note: This post was a response in a separate cross-posted thread.Ok, I think I got it. Since they are distinct numbers, the first digit can be chosen in 9 ways (except 0) while the second can also be chosen in 9 ways, making it 81 numbers instead of 90.. So am I right this time?
Homework Statement
An intelligence agency forms a code of two distinct digits selected from 0, 1 , 2…, 9, such that the first digit of the code is nonzero. The code, handwritten on a slip, can, however, potentially create confusion when read upside down - for example; the code 91 may appear as...