24 from 8,8,3,3 Puzzle - Solution
The Puzzle:
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
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