*This post is based on Hindi colloquial/conversational number pairs used in approximating a quantity. Knowledge of colloquial Hindi is requisite.*

Hindi conversational numbering follows Hindu-Arabic Decimal Number System with Hindi pronunciations. One (1) becomes

*Ek*, Two (2) becomes

*Do*, Three (3) becomes

*Teen*and so on. When asked to approximate a quantifiable noun viz. in response to “how many minutes before the dad comes home?”, Hindi speakers often speak in number pairs such as

*Ek*-

*Do*(1-2). Not all pairs are acceptable and feel “right” when you say them aloud. This post will try to discern if there is a mathematical pattern in acceptable set of pairings.

Pair | Type |

1-2 | Next |

2-1 | One |

2-3 | Next |

2-4 | Double, Next 2x |

2-5 | Plus 3 |

3-1 | One |

3-4 | Next |

4-1 | One |

4-5 | Next |

4-6 | Next 2x |

5-1 | One |

5-6 | Next |

5-10 | Double, Next 5x |

6-1 | One |

6-7 | Next |

7-1 | One |

7-8 | Next |

8-1 | One |

8-9 | Next |

8-10 | Next 2x |

9-1 | One |

9-10 | Next |

10-1 | One |

10-11 | Next |

10-12 | Next 2x |

10-15 | Next 5x |

10-20 | Double, Next 10x |

11-1 | One |

11-12 | Next |

12-1 | One |

12-13 | Next |

12-15 | Plus 3 |

13-1 | One |

13-14 | Next |

14-1 | One |

14-15 | Next |

15-1 | One |

15-16 | Next |

15-20 | Next 5x |

16-1 | One |

16-17 | Next |

17-1 | One |

17-18 | Next |

18-1 | One |

18-19 | Next |

18-20 | Next 2x |

19-1 | One |

19-20 | Next |

20-1 | One |

20-21 | Next |

20-22 | Next 2x |

20-25 | Next 5x |

20-30 | Next 10x |

21-1 | One |

21-22 | Next |

22-1 | One |

22-23 | Next |

22-25 | Plus 3 |

23-1 | One |

23-24 | Next |

24-1 | One |

24-25 | Next |

25-1 | One |

25-26 | Next |

25-30 | Next 5x |

25-50 | Double |

26-1 | One |

26-27 | Next |

27-1 | One |

27-28 | Next |

28-1 | One |

28-29 | Next |

28-30 | Next 2x |

29-1 | One |

29-30 | Next |

30-1 | One |

30-31 | Next |

30-32 | Next 2x |

30-35 | Next 5x |

30-40 | Next 10x |

31-1 | One |

31-32 | Next |

32-1 | One |

32-33 | Next |

32-35 | Plus 3 |

33-1 | One |

33-34 | Next |

34-1 | One |

34-35 | Next |

35-1 | One |

35-36 | Next |

35-40 | Next 5x |

36-1 | One |

36-37 | Next |

37-1 | One |

37-38 | Next |

38-1 | One |

38-39 | Next |

39-1 | One |

39-40 | Next |

40-1 | One |

40-41 | Next |

40-42 | Next 2x |

40-45 | Next 5x |

40-50 | Next 10x |

After manual enumeration of all such pairs where first number is up to 40, we can observe following seven type of pairings:

**Next**: This is the most common type of pair in which each number is paired with next whole number following it.**One**: This is the second most common type of pair in which each number is paired with number One, except, of course, number One itself.**Next 2x**: Numbers 2, 4, 8, 10, 18, 20, 28, 30 and 40 pair with next number which is multiple of 2 i.e. next even number. Primarily, numbers ending in 0 seem to follow this pairing. There is temporary pairing of this type for numbers ending in 8 but this doesn’t continue long since after 38 this doesn’t work. 2 and 4 are obvious exceptions.**Plus 3**: 2, 12, 22 and 32 seem to follow this type of pairing. Projecting further, it appears that all numbers ending in 2 would following this pairing.**Next 5x**: 5, 10, 15, 20, 35 and 40 predictably follow pattern of paring with next number which is multiple of 5. These numbers themselves are multiple of 5 clearly following a pattern.**Next 10x**: 10, 20, 30 and 40 again following pattern of pairing with next number which is multiple of 10 while themselves being multiple of 10.**Double**: Numbers 2, 5, 10 and 25 pair with numbers twice them though 2, 5 and 10 be also be categorized to other pairing types which makes more sense. Projecting beyond 40, we see that while 50 doesn’t follow this pairing, 100, 150, 200, 500 do so. There doesn’t seem to be any identifiable pattern here.

I also tried to find pattern in sum, product and ratio of numbers in these pairs and in ratio of consecutive sums and consecutive products without success. Possibly, enumerating pairs after 40 may identify more types of pairings. What are your thoughts and observations?

(Peculiarity of such pairings have been in mind for quite many years but this post on Futility Closet — which, by the way, is a recommended read blog — propelled me to write this post.)

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