This is in continuation of Closest to pi.

(A) As we are aware, the approximate value of e with some decimals is 2.7182818284590...

Write an expression using all digits (0-9) once each, to achieve the closest value to e. The digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 must be arranged strictly in this order. You can only use the five symbols: parentheses , addition, subtraction, multiplication and division symbols that is, (), +, -, *, /

Concatenating two or more digits is allowed. Each symbol can occur at most once in the given expression. Only standard order of operations is followed – that is, multiplication does not take precedence over division, addition does not take precedence over multiplication, and so on.

For example : (123+456)/7890 is a valid expression. However, expressions like 1+234/567 + 8/9 -0 or, 1+3*2456/78-90 are not allowed.

(B) Write an expression closest to e, if all the other conditions in (A) remain unaltered, but the restriction of each symbol occurring at most one is withdrawn. For example, expressions like 1+234/567 + 8/9 -0 is allowed. However, expressions like: 1+3*2456/78-90 are not allowed.

(C) What are the respective answers to (A) and (B) if a sixth symbol, that is, the decimal point is allowed?

A) 123/45 - (6789*0) = 2.733...

Posted by Dej Mar on 2012-04-18 13:59:01