Equations Goals

SW Goals

1. Asw + Bsw = (B ± A)(A x B)

2. AB÷(CB±1) = A÷(C±Bsw)

3. AB ÷ (C x (A ± B)) = Csw÷(Asw ± Bsw)

Ways to hide goals to make it harder to see the trick:

1. Multiplying by 1 (multiply by 

2. 22,33,44, etc) so the first step if you see a fraction on the goal line is to see if the fraction can be simplified

3. Flip the fraction (1330 becomes 3013) this makes your solution longer

4. Do 1 - goal, 2 - goal, 1 + goal, etc this also makes your solution longer

Factor-Rearrangment (mostly x and division)

96×84 = 8! ÷ 5

96x81= 6^5

(6^4)x5= 6! x 9

84 × 36 = 9! ÷ 5!

36 × 80 = 5! x 4!

72 × 40 = 5! x 4!

63 × 48 = 9! ÷ 5!

42 × 72 = 9! ÷ 5!

20 × 84 = 8! ÷ 4!

30 × 56 = 8! ÷ 4!

40 × 42 = 8! ÷ 4!

60 × 28 = 8! ÷ 4!

80 × 21 = 8! ÷ 4!

6! x 28 = 8! ÷ 2

6! x 84 = 9! ÷ 6

9! ÷ 24 = 7! x 3

9! ÷ 84 = 6! x 6

(27^5) x 3 = 9^8

48 × 27 = 6^4

Factorial Goals without MOP

(6!²) x 7 = 10!

(6!²) x 77 = 11!

(7!²) ÷ (10!) = 7

10!÷7 = 6!²

10! x 7 = 7!²

10! ÷ (6!²) = 7

10! ÷ 6! = 7!

11! x 77 = 7!^2

11! ÷ 77 = 6!^2

√(10! ÷ 7) = 6!

√(11! ÷ 77) = 6!

√(10! x 7) = 7!

√(11! x 77) = 7!

√(10! ÷ 63) = 6! ÷3

√(10! x 28) = 7! x 2

9! x 70 = 7!²

45 × 64 = 5! x 4!

6! x 6 = 45 × 96

5!√(16 ^ 6!) = 8^8

√(8! + 81) = 201

√(6! × 45) = 180

√((7!➗ 3) + 1) = 4!

(29 ^ 2) x 6 = 7! + 3!

(82 ^ 2) x 6 = 8! + 4!

5 × (84 ^ 2) = 8! - 7!

 88 √ 3 ^ 6 =  3^9

9➗ (25 + 5_SW) = 2sw - 7sw

Factorial Goals with MOP

√(8! x 9!) = 8! x 3

√(9! x 8!) = 9! ÷ 3

7! x 9 = 8! + 7!

6! × 57 = 8! + 6!

(5! x 48) - 7! = 6!

8 ÷ 73 = 8! ÷ (9! + 7!)

(6! -1)! ÷ 56 = 6!! ÷ (8!)

(7! - 1)! x 42 = 7!! ÷ (5!)

(8! - (7!)) ÷ 49 = 6!

(8! + (7!)) ÷ 63 = 6!

(7! x (8!)) x 80 = 10!

(9! ÷ 63) - (7!) = 6!

6! x 7! = 10!

√(7! + 1) = 71

√(48! x 49!)) = = 48! x 7

Root/Star Identities (2 powers ^ ^)

2 ÷ (3^17) = 6 ÷ (9^9)

3 ÷ (8^5) = 6 ÷ (4^8)

8sw ÷ (4^8) = 4 ÷ (8^7) (yes)

6sw ÷ (4^7) = 3sw ÷ (8^5) (yes)

80 ÷ (8^6) = 5 ÷ (4^7)

6 ÷ (9^5) = 2 ÷ (3^9)

8 ÷ (16^8) = 4sw ÷ (8^9) (yes)

1 ÷ (2^23) = 4sw ÷ (8^7) (yes)

b√(a^c^d) = a^((c^d)/b)

47 × 51 = (7^4) - 4 (difference of squares)

91 × 72 = (3^8) - 9

Root/Star Identities with ! (2 powers ^ ^)

8 x (5!^4) = 4^(6!) (yes)

64^(5! x 7) = 2^(7!) (yes)

8^(48 x (7!)) = 4^9! (yes)

2 ÷ (3^13) = 6÷(9^7)

(9 × 27)^4 = 9^8

(8^7)÷32 = 4^8

(6√27)^8 = 3^4

(5!√27)^6! = 9^9

Root/Star Identities with ! (2 powers ^ ^ and 1 root √)

2^(5! x 63) = √(8^(7!))

49^(7!) = √√(7^(8!)) (need mop)

5!√(16^(6!)) = 8^8

√(48! x (49!)) = 48! x 7 (need mop)

√(9! x (8!)) = 9! ÷ 3 (need mop)

√(8! x (9!)) = 8! x 3 (need mop)

My Fav 🥰 Ones √

√((9!^3) ÷ (8!)) = 9! x 3

√((8!^3) ÷ 9!) = 8! ÷ 3

√((7!) x 8!) ÷ 2) = 7! x 2

√((7!) x 8!) x 2) = 7! x 2

√((7!) x 9!) ÷ 2) = 7! x 6

√((7!) x 9!) ÷ 2) = 7! x 8

9! x 70 = 7!^2

6√(8^8) = 13

8√(81^6) = 27

√(3!! + 9) = 27

4√(6! + 9) = 9

6√(6! + 9) = 3

Percent Goals (2 roots, and ^)

(2√(UD)6)√(UD)4 = 3÷(5^4)

(2√(UD)4)√(UD)2 = 1÷(5^4)

50√(8^7) = 2^(6√(UD)

9√(9^50) = (3√(UD)3)√3

7√(2^25) = (7√(UD)8)√4

a√(UD)b√(UD)√c = d÷(5^4): if a x b x c= 16 x d

Goal: 5_SW % 5_SW % 96

Solution: 6 ÷ (5 ^ 6)

9 percent (4 ÷ 9) = 2 percent 2

Middle Root/Star Identities with ! (2 roots √√)

27^√(8!) = 3^(√(9!))

(√(5sw - 9sw))√9 = 3^(√45)

27^√(8!) = 3^√(9!)

25^(3√(7!)) = 5^(3√(8!))

(4×7!)√2 = 8!√4

(5!x4)√4 = 6!√8

(7!x48)√4

7!√(3^6!) = 7√3

√(7!) = 12 x √35

8^(√(8!)) = 2^(√(9!))

2^√(9! x 9) = (√(8!))√(2^(9!))

MOP Goals

32√3 = √√√√√3

(8^7)√8 = √√√√√√√√√√√√√√√√√√√√√8

80√7 = √√√√(5√7)

(48^2)√6 = √√√√√√√√(9√6)

64√3 = √√√√√√3

96√8 = √√√√√2

MOP √ + sw

78√3 = (5 - 8sw)√√√√√3

73√2 = (9 + 8sw)√√√√2

K=6 Goals (÷ ÷ ^)

6 - (7 ÷ 6) = (5^5) ÷ 6

K=7 Goals (÷ ÷ ^)

5 + 7sw = (8^5) ÷ 7

49 ÷ 8(upside down) = (7^(5^6))÷8

4 - 2sw = (7^9)÷2

K=8 Goals

1 ÷ 5 = (7^8)÷5

4-7sw = (3^9)÷7 (no)

97÷8 = (9^4)÷8

(9÷8)-7 = (7^6)÷8

8 ÷ 9 = (8^(3 × 7)) ÷ 9

8(upside down) ÷ 9 = (8^(6^5)÷9 (no)

K=9 Goals

(8÷9)-3 = (8^7)÷9

1-(1÷9) = (8^(5^6)÷9

9 ÷ 8 = (9^7)÷8

4 + (7sw x 9sw) = (8^8) ÷ (7 × 9)

K=10 Goals

3 ÷ 8 = (3^9) ÷ 8

K=6, 7, 11 Goals

K7: 5 + 7sw = (8^5) ÷ 7 (no)

K7: 3 + 7sw = (8^(3^7) ÷ 7 (no)

k6: 6 - (7 ÷ 6) = (5^5) ÷ 6 (yes)

k7: 49 ÷ 8up = (7^(5^6)) ÷ 8 (no)

k6: 5 + 7sw = (6^ (4x(5^9)÷8 (no)

k7: 4 - 2sw = (7^9) ÷ 2 (no)

K formulas

Average

(A + B) + C = (A + B + 2C) / 4

Root of Root

√ (3 + √8) = √2 + 1

√ (3 - √8) = √2 - 1

√ (6 + √32) = √2 + 2

√ (6 - √32) = 2 - √2

√ (4 + √12) = √3 + 1

√ (4 - √12) = √3 - 1

√ (7 + √48) = √3 + 2

√ (7 - √48) = 2 - √3

√ (6 + √20) = √5 + 1

√ (6 - √20) = √5 - 1

√ (9 + √80) = √5 + 2

√ (9 - √80) = √5 - 2

√ (41 + √6!) = √ (41 + √720) = √5 + 6 (requires factorial)

√ (41 - √6!) = √ (41 + √720) = 6 - √5 (requires factorial)

√ (7 + √24) = √6 + 1 (optional factorial)

√ (7 - √24) = √6 - 1 (optional factorial)

√ (8 + √28) = √7 + 1

√ (8 - √28) = √7 - 1

√ (9 + √32) = √8 + 1 (don’t oversimplify √32)

√ (9 - √32) = √8 - 1 (don’t oversimplify √32)