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> Just Math (2)> Science> Algorithms
Consider numbers like 343 or 2592.
343=(3+4)^3
2592=2^5*9^2.

We have just shown that some numbers stay unchanged when a number of mathematical operators are added /inserted, without changing the order of the digits.
Within our puzzle lets call those numbers expressionist numbers.
Let us limit the set of acceptable mathematical symbols to the following operators: +, -, *, /, ^, sqrt, !. and any amount of brackets.

My questions:
In the period between 10 A.D. & 2016 A.D. what years were labeled by expressionist numbers?
How many such years will there be between 2017 A.D. & 9999 A.D.?

Bonus: How about one, two (or more) 5-digit examples?

(No Solution Yet, 1 Comments) Submitted on 2016-05-30 by Ady TZIDON   
Difficulty: 3 of 5 Bonus: As simple as it gets (in Liars and Knights) Rating: 4.50
In Tripleland, natives always go in trios: a knight, a knave, and a liar.

Once I met such a trio, and I asked one of the natives a simple question ("simple" meaning, "of six words or less"); he answered, and I knew what type he was. Then, I asked another of the natives a different simple question; he answered, and I knew what type he was, and therefore, the type of the third one too.

"Logical" thinking: This cannot be. The natives could be in six possible orders. Two yes-no questions allow four combinations. Thus, you cannot pick one out of six with only two questions; you need one more!

How could this be? What's wrong with the reasoning above?

(Solution Posted, 6 Comments) Submitted on 2006-09-02 by Federico Kereki   
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