| No. | Formule (Type I) | #1 | #24 |
| 1.1 | ((a + b) + c) + d = r | 0 | 27 |
| 1.2 | ((a + b) + c) - d = r | 31 | 4 |
| 1.3 | ((a + b) - c) - d = r | 140 | 0 |
| 1.4 | ((a - b) - c) - d = r | 16 | 0 |
| 1.5 | ((a + b) + c) * d = r | 0 | 24 |
| 1.6 | ((a + b) + c) : d = r | 23 | 3 |
| 1.7 | ((a + b) - c) * d = r | 25 | 117 |
| 1.8 | ((a + b) - c) : d = r | 95 | 0 |
| 1.9 | ((a - b) - c) * d = r | 16 | 17 |
| 1.10 | ((a - b) - c) : d = r | 23 | 0 |
| 1.11 | ((a + b) * c) + d = r | 0 | 38 |
| 1.12 | ((a + b) * c) - d = r | 35 | 41 |
| 1.13 | ((a - b) * c) + d = r | 150 | 54 |
| 1.14 | ((a - b) * c) - d = r | 91 | 30 |
| 1.15 | ((a + b) : c) + d = r | 0 | 3 |
| 1.16 | ((a + b) : c) - d = r | 88 | 0 |
|
| No. | Formule (Type I) | #1 | #24 |
| 1.17 | ((a - b) : c) + d = r | 117 | 0 |
| 1.18 | ((a - b) : c) - d = r | 29 | 0 |
| 1.19 | ((a * b) + c) + d = r | 0 | 45 |
| 1.20 | ((a * b) + c) - d = r | 38 | 58 |
| 1.21 | ((a * b) - c) - d = r | 48 | 25 |
| 1.22 | ((a : b) + c) + d = r | 0 | 3 |
| 1.23 | ((a : b) + c) - d = r | 101 | 0 |
| 1.24 | ((a : b) - c) - d = r | 19 | 0 |
| 1.25 | ((a + b) * c) * d = r | 0 | 22 |
| 1.26 | ((a + b) * c) : d = r | 27 | 51 |
| 1.27 | ((a + b) : c) : d = r | 56 | 0 |
| 1.28 | ((a - b) * c) * d = r | 8 | 57 |
| 1.29 | ((a - b) * c) : d = r | 116 | 20 |
| 1.30 | ((a - b) : c) : d = r | 29 | 0 |
| 1.31 | ((a * b) + c) * d = r | 0 | 29 |
| 1.32 | ((a * b) + c) : d = r | 29 | 12 |
|
| No. | Formule (Type I) | #1 | #24 |
| 1.33 | ((a * b) - c) * d = r | 13 | 55 |
| 1.34 | ((a * b) - c) : d = r | 56 | 9 |
| 1.35 | ((a : b) + c) * d = r | 0 | 72 |
| 1.36 | ((a : b) + c) : d = r | 116 | 0 |
| 1.37 | ((a : b) - c) * d = r | 29 | 16 |
| 1.38 | ((a : b) - c) : d = r | 27 | 0 |
| 1.39 | ((a * b) * c) + d = r | 0 | 10 |
| 1.40 | ((a * b) * c) - d = r | 14 | 10 |
| 1.41 | ((a * b) : c) + d = r | 0 | 19 |
| 1.42 | ((a * b) : c) - d = r | 104 | 9 |
| 1.43 | ((a : b) : c) + d = r | 0 | 0 |
| 1.44 | ((a : b) : c) - d = r | 15 | 0 |
| 1.45 | ((a * b) * c) * d = r | 1 | 5 |
| 1.46 | ((a * b) * c) : d = r | 14 | 29 |
| 1.47 | ((a * b) : c) : d = r | 54 | 4 |
| 1.48 | ((a : b) : c) : d = r | 14 | 0 |
|
| No. | Formule (Type II) | #1 | #24 |
| 2.1 | (a - (b * c)) + d = r | 55 | 0 |
| 2.2 | (a - (b * c)) - d = r | 22 | 0 |
| 2.3 | (a - (b : c)) + d = r | 32 | 0 |
| 2.4 | (a - (b : c)) - d = r | 100 | 0 |
| 2.5 | (a - (b * c)) * d = r | 11 | 18 |
| 2.6 | (a - (b * c)) : d = r | 29 | 0 |
| 2.7 | (a - (b : c)) * d = r | 45 | 71 |
| 2.8 | (a - (b : c)) : d = r | 116 | 0 |
| 2.9 | (a : (b + c)) + d = r | 0 | 0 |
| 2.10 | (a : (b + c)) - d = r | 5 | 0 |
| 2.11 | (a : (b - c)) + d = r | 78 | 0 |
| 2.12 | (a : (b - c)) - d = r | 72 | 0 |
| 2.13 | (a : (b + c)) * d = r | 56 | 2 |
| 2.14 | (a : (b + c)) : d = r | 27 | 0 |
| 2.15 | (a : (b - c)) * d = r | 29 | 28 |
| 2.16 | (a : (b - c)) : d = r | 116 | 0 |
|
| No. | Formule (Type III) | #1 | #24 |
| 3.1 | (a + b) * (c + d) = r | 0 | 14 |
| 3.2 | (a + b) * (c - d) = r | 0 | 70 |
| 3.3 | (a - b) * (c - d) = r | 36 | 21 |
| 3.4 | (a + b) : (c + d) = r | 95 | 0 |
| 3.5 | (a + b) : (c - d) = r | 23 | 0 |
| 3.6 | (a - b) : (c + d) = r | 23 | 0 |
| 3.7 | (a - b) : (c - d) = r | 86 | 0 |
| 3.8 | (a * b) + (c * d) = r | 0 | 17 |
| 3.9 | (a * b) + (c : d) = r | 0 | 10 |
| 3.10 | (a : b) + (c : d) = r | 34 | 0 |
| 3.11 | (a * b) - (c * d) = r | 29 | 24 |
| 3.12 | (a * b) - (c : d) = r | 29 | 16 |
| 3.13 | (a : b) - (c * d) = r | 17 | 0 |
| 3.14 | (a : b) - (c : d) = r | 101 | 0 |
|
| No. | Formule (Type IV) | #1 | #24 |
| 4.1 | a - ((b * c) * d) = r | 12 | 0 |
| 4.2 | a - ((b * c) : d) = r | 101 | 0 |
| 4.3 | a - ((b : c) : d) = r | 27 | 0 |
| 4.4 | a - ((b + c) * d) = r | 22 | 0 |
| 4.5 | a - ((b + c) : d) = r | 92 | 0 |
| 4.6 | a : ((b + c) + d) = r | 23 | 0 |
| 4.7 | a : ((b + c) - d) = r | 95 | 0 |
| 4.8 | a : ((b - c) - d) = r | 23 | 0 |
| 4.9 | a : ((b * c) + d) = r | 29 | 0 |
| 4.10 | a : ((b * c) - d) = r | 56 | 0 |
| 4.11 | a : ((b : c) + d) = r | 116 | 0 |
| 4.12 | a : ((b : c) - d) = r | 27 | 7 |
|
| No. | Formule (Type V) | #1 | #24 |
| 5.1 | a - (b : (c + d)) = r | 27 | 0 |
| 5.2 | a : (b - (c * d)) = r | 29 | 0 |
| 5.3 | a : (b - (c : d)) = r | 116 | 11 |
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Toelichting
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#1 betekent aantal viertallen die 1 opleveren door gebruik te maken van die formule
Voorbeeld
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2.10 : #1 (Aantal oplossingen is 5)
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1. (4 : (1 + 1)) - 1 = 1
2a. (6 : (2 + 1)) - 1 = 1
2b. (6 : (1 + 1)) - 2 = 1
3a. (8 : (3 + 1)) - 1 = 1
3b. (8 : (1 + 1)) - 3 = 1
4. (8 : (2 + 2)) - 1 = 1
5. (9 : (2 + 1)) - 2 = 1
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Bij 2a en 2b worden weliswaar verschillende oplossingen
weergegeven, maar dit gebeurt met hetzelfde viertal. Om redenen van efficientie
wordt een dergelijke oplossing slechts eenmaal meegeteld.
#24 betekent aantal viertallen die 24 opleveren door gebruik te maken van die formule
Voorbeeld
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1.22 : #24 (Aantal oplossingen is 3)
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1a. ((6 : 1) + 9) + 9 = 24
1b. ((9 : 1) + 6) + 9 = 24
2a. ((7 : 1) + 8) + 9 = 24
2b. ((8 : 1) + 7) + 9 = 24
2c. ((9 : 1) + 7) + 8 = 24
3. ((8 : 1) + 8) + 8 = 24
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formule I is van het type ((a # b) # c) # d
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formule II is van het type (a # (b # c)) # d
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formule III is van het type (a # b) # (c # d)
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formule IV is van het type a # ((b # c) # d)
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formule V is van het type a # (b # (c # d))
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