Question

Using the integers -5 to 5, at most one time each, write an expression that will have the greatest or least absolute value

Answer 1

• very large: (2 -(-1))^(1 -(-2))^(3 -(-3))^(4 -(-4))^(5 -(-5))^0
• smallest: 0(5+4+3+2+1+(-1)+(-2)+(-3)+(-4)+(-5)) = 0

Explanation:

Exponentiation gets you to large numbers really fast. This may not be the largest possible with these numbers, but it is certainly very large.

(2 -(-1))^(1 -(-2))^(3 -(-3))^(4 -(-4))^(5 -(-5))^0

Exponents are evaluated right to left, so this becomes ...

3^3^6^8^10 = 3^3^6^1073741824

The next level of evaluation, 6^1073741824, is a number with more than 835 million digits. I cannot compute the number of digits in the final value of this expression.

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Of course, the smallest magnitude is achieved by multiplying by 0.

smallest = 0·(5 + 4 + 3 + 2 + 1 +(-1) +(-2) +(-3) +(-4) +(-5)) = 0