The two series a₁, a₂, ……… and b₁, b₂, ……. are two arithmetic progressions, where a₁+ b₁= 100 and a₂₄– a21= b₉₇– b₁₀₀.  Find the sum of the 100 terms  (a₁+ b₁₀₀), (a₂+ b₉₉),…………. (a₁₀₀+ b₁).

How is Venkat’s brother’s father’s brother’s father’s daughter’s sister’s daughter’s brother related to Venkat?

Mr. Baha Man had locked his pet dogs in his room and instructed his three sons – Woof, Arf and Grrr – to keep a watch over them while he was away. When he came back, he found that there were no dogs in the room. When he came to know that exactly one of his sons had let the dogs out, he angrily shouted at them, “WHO LET THE DOGS OUT?” Frightened, each son gave two replies to the question, as given below:
Woof : Arf did. Grrr didn’t.
Arf : I didn’t. Woof did.
Grrr : Woof didn’t. Arf didn’t.
If it is known that of the statements given by each son at least one was true, then which son let the dogs out?