riddle - An Age Old Problem

It was Joshua's birthday party and being a surprisingly clever lad for his age he decided to challenge his friends to a little game.

"If anyone can guess the number I'm thinking of they will get a special prize!" he announced.

"I will give you just four clues," he continued.

"One. It is made up of five distinct, non-zero digits.

"Two. The first two digits form the square of the third.

"Three. The last two digits form a number one less than the square of my age.

"Four..."

However before he could give the final clue, Jemma being an equally astute little girl, shouted out the answer with 100% certainty that she was correct and thus claimed the prize.

What was the number Joshua was thinking of?

Originally posted by tommyg007
It was Joshua's birthday party and being a surprisingly clever lad for his age he decided to challenge his friends to a little game.

"If anyone can guess the number I'm thinking of they will get a special prize!" he announced.

"I will give you just four clues," he continued.

"One. It is made up of five distinct, non-zero digits.

"Two. ...[text shortened]... that she was correct and thus claimed the prize.

What was the number Joshua was thinking of?

18324.

81924.

By clue 1 & 2, the first digits must be 164, 255, 366, 497, 648, or 819.

By clue 3, the last two digits must be 15, 24, 35, 48, or 63.

If you combine all the combinations that do not let a digit repeat:
16435, 49715, 49735, 49763, 64815, 64835, 81924, 81935, 81963,
and you know the girl, who knew the boy's age, would know the last two digits, it must be the possibility with the unique last two digits, i.e., 81924

Correct!! A gold star to Elias5891 😀

Originally posted by tommyg007
Correct!! A gold star to Elias5891 😀

Oops I misread the question. I thought that the first two digits squared formed the last three digits.

Interestingly enough my answer is the unique solution if read that way.
18^2 =324

5^2 - 1= 24