# 24 from 8,8,3,3 Puzzle - Solution

## The Puzzle:

How can I get the answer 24 by only using the numbers 8, 8, 3 and 3.

You can use add, subtract, multiply, divide, and parentheses.

Bonus rules: also allowed are logarithms, factorials and roots

(Puzzle supplied by "Steve123")

## Our Solution:

1) Supplied by "mathsyperson":
8/(3-(8/3))
= 8/(1/3)
= 24

2) Supplied by "puzzler09" (using bonus rules):
((8 x 3!)/3)+8
= ((8 × 3 × 2 × 1)/3)+8
= (48/3)+8
= (16)+8
= 24

3) Supplied by "Mark" (using bonus rules):
(3!/∛8)*8

4) Supplied by "Daryl S" (using bonus rules):
(8-3)!/(8-3)
(∛8 × ∛8)!
(∛8 + ∛8)!
√(8×8×3×3)
8+(8×(3!/3))
((√(8+8) × (3/3))!
√(8+8) × (3+3)
(log base(3!/3) of 8) × 8
((log base(3!/3) of (8+8))!

5) Supplied by "Sunil Prajapati" (using bonus rules):
√(8×8)×√(3×3) which is a variation of √(8×8×3×3) by Daryl S

6) Supplied by "Robert Veith" (using bonus rules):
(3! - 3) x √(8 × 8)
(3 + (3(8 - 8))!)!
(3! - 3 + 8/8)!
(3! - 3 + (8 - 8)!)!
(3! x 8)/(8 - 3!)
(3 + ∛(8 - 8)!)!
(3 + ∛(8/8))!
3!/(3/8) + 8 = 24

38 - 8 - 3!
3! × ∛(8 × 8)
(8 + 8 - 3! - 3!)!
(8 - 3! + ∛8)!
(√(8 + 8 + 3 - 3))!
((8 - 3!)(∛8))!
8 × 3! - 8 × 3
(3! + 3!) × √(√(8 + 8))
(3 + 3 - √(√(8 + 8)))!
(3! - 3)! × √(8 + 8)
√(3! × 3!) × √(8 + 8)
(8/(8 - (√(3! + 3))!))!
(8/(8 - √(3! × 3!)))!
(8/(8 - 3 - 3))!
(8/(8 - (3! - 3)!))!
(8/(8 - (√(3 × 3))!))!
(√3! × 3!) - √(√(8 + 8)))!
(√((8 - √(3! × 3!)) × 8))!
(3! - √(8/(8 - 3!)))!
(√(3! + 3) + 8/8)!
(√(3! + 3) + (8 - 8)!)!
(√((8 - (√3! + 3))!) × 8))!
(√((8 - (√(3 × 3))!) × 8))!
(√((8 - (3! - 3)!) × 8))!
3! × √(8 × ∛8)
((8 - 3!)(8 - 3!))!
(√(3 × 8/3 + 8))!
(3! × 8)/∛8
(3! × ∛8 - 8)!
3! × √(8∛8)
√(8 + 8) × (√(3! + 3))!
((3 - 3)! × √(8 + 8))!
8√((3 × 3)!/8!)
(√(8 × 8)/(3!/3))!
(3! - 3) × √(8 × 8)
√(3! + 3) × √(8 × 8)
8√((3! + 3)!/8!)
-8 × (log base(3/3!) of 8)
(-(log base(3/3!) of (8 + 8)))!
(√(8 + 8) × (log base(3) of 3))!
(√(3! + 3) + (log base(8) of 8))!
(√(3 × 3) + (log base(8) of 8))!
(3 + (log base(8) of 8)) × 3!
(3! - 3 + (log base(8) of 8))!
(3! - √(3 + (log base(8) of 8)))!
(3 + ∛(log base(8) of 8))!
(√(8 + 8 × (log base(3) of 3)))!
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