All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
A rare event (Posted on 2010-07-03) Difficulty: 2 of 5
This year (by June 2010) IT already happened thrice and will occur one more time, on October 1st.

Next time SAME THING will occur on two different dates in 2011 and on 6 different dates in 2012.

In 2013 - only during one day and then in the following years IT will present itself at least once a year till 2036.

In 2037 - not even once.

What is IT (a.k.a. SAME THING )?
If IT = f(YEAR) what is f(2020)?
In what year in this century f(YEAR) is maximal?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: What IT is (parts 1 and 2) (spoiler) | Comment 2 of 3 |
(In reply to What IT is (parts 1 and 2) (spoiler) by Steve Herman)

f(2060) is only 6 as month 2 has only 29 days.

7 is indeed the maximum, though, in 2024, having months 1, 2, 3, 4, 6, 8 and 12.

(Not that I was able to figure out the rule, but once you got the rule, I could produce the table below.)

01  1          34  1          67  0
02  2          35  2          68  1
03  2          36  6          69  1
04  3          37  0          70  3
05  2          38  1          71  0
06  4          39  1          72  6
07  2          40  5          73  0
08  4          41  0          74  0
09  3          42  4          75  2
10  4          43  0          76  1
11  2          44  3          77  2
12  6          45  3          78  2
13  1          46  1          79  0
14  3          47  0          80  4
15  3          48  6          81  2
16  4          49  1          82  0
17  1          50  3          83  0
18  5          51  1          84  5
19  1          52  2          85  1
20  5          53  0          86  0
21  3          54  4          87  1
22  3          55  2          88  3
23  1          56  4          89  0
24  7          57  1          90  5
25  2          58  0          91  1
26  2          59  0          92  1
27  3          60  6          93  1
28  4          61  0          94  0
29  1          62  0          95  1
30  6          63  3          96  4
31  1          64  2          97  0
32  3          65  1          98  1
33  2          66  3          99  2

produced by

DEFDBL A-Z
CLS
DIM l(12)
DATA 31,28,31,30,31,30,31,31,30,31,30,31
FOR i = 1 TO 12: READ l(i): NEXT

FOR i = 1 TO 99
  IF i MOD 4 = 0 THEN l(2) = 29:  ELSE l(2) = 28
  ct = 0
  FOR mo = 1 TO 12
    d = i / mo
    IF d = INT(d) THEN
      IF d <= l(mo) THEN ct = ct + 1
      c = INT((i - 1) / 33): r = (i - 1) MOD 33
      c = c * 15 + 1
      r = r + 1
      LOCATE r, c
      PRINT USING "## ##"; i; ct
    END IF
  NEXT
NEXT


  Posted by Charlie on 2010-07-03 16:20:22
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information