The Threes Puzzle

“Daddy, I’d like to have the little red bicycle you see in the shop window over there,” Lenny said pointing, as they were taking a walk along the avenue.

“Sure, Lenny,” said daddy, “If you can solve a little puzzle, I’ll buy it for you right away.”

“Yippee, daddy,” said Lenny enthusiastically, jumping up and down, “tell the puzzle to me right away.”

“Take the number 3 and multiply it by itself 999 times. Then tell me the last digit of the resulting number, Lenny?”

“Hmm…,” said Lenny. “Let’s sit down on that park bench so I can figure it out.”

“Ok, Lenny, take your time,” said daddy.

Lenny sat on the bench with daddy for some minutes with a very concentrated look on his face. Then he brightened up and said “I’ve got the answer, daddy.”

As the answer was correct, they went to the bicycle shop and Lenny came out riding the little red bicycle with a big smile on his face.

What would you say is the last digit in the number resulting from multiplying 3 by itself 999 times?

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