Return to Question

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

Hint 6:

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

Hint 6:

Hint 7:

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

Hint 6:

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.}

If a number conforms to a special rule, I call it a BEN Number™.
Use the following examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ BEN }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 17 }&\text{ 57 }\\ \hline \text{ 20 }&\text{ 60 }\\ \hline \text{ 24 }&\text{ 64 }\\ \hline \text{ 49 }&\text{ 89 }\\ \hline \text{ 121 }&\text{ 161 }\\ \hline \text{ 158 }&\text{ 198 }\\ \hline \text{ 538 }&\text{ 578 }\\ \hline \text{ 830 }&\text{ 870 }\\ \hline \text{ 1,059 }&\text{ 1,099 }\\ \hline \text{ 1,144 }&\text{ 1,184 }\\ \hline \text{ 1,622 }&\text{ 1,662 }\\ \hline \text{ 2,345 }&\text{ 2,385 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

BEN Numbers™,Not BEN Numbers™
17,57
20,60
24,64
49,89
121,161
158,198
538,578
830,870
1059,1099
1144,1184
1622,1662
2345,2385

Bonus Question:
It's true that the cardinality of BEN Numbers' set is finite. What is the largest BEN Number?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5: