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

Home > Numbers
THREE Triangular Numbers (Posted on 2008-10-21) Difficulty: 3 of 5
Tom, Dick and Harry each chose a different 5-digit triangular number whose digits fell into the pattern THREE, where each different letter represents a different base-10 digit.

Dick's triangular number had no digit in common with either Tom's or Harry's.

What was Dick's number? What two triangular numbers did the other two choose?

  Submitted by Charlie    
Rating: 2.0000 (1 votes)
Solution: (Hide)
The only 5-digit triangular numbers of the form THREE are:

15400
17955
27966
40755
58311
75466
79800
84255
95266

Only 27966 consists of digits such that two of the other numbers contain no digits in common with it, and therefore 27966 is Dick's number, with 15400 and 58311 being the other two numbers.

adder = 1
DO
 triNum = triNum + adder
 adder = adder + 1
 n$ = LTRIM$(STR$(triNum))
 IF LEN(n$) = 5 THEN
  IF INSTR(2, n$, MID$(n$, 1, 1)) = 0 THEN
  IF INSTR(3, n$, MID$(n$, 2, 1)) = 0 THEN
  IF INSTR(4, n$, MID$(n$, 3, 1)) = 0 THEN
   IF MID$(n$, 4, 1) = MID$(n$, 5, 1) THEN
     PRINT n$
     ct = ct + 1: tn$(ct) = n$
   END IF
  END IF
  END IF
  END IF
 END IF
LOOP UNTIL LEN(n$) > 5

PRINT

FOR i = 1 TO ct
  goodCt = 0
  REDIM m$(10)
  FOR j = 1 TO ct
    good = 1
    FOR k = 1 TO 5
     IF INSTR(tn$(j), MID$(tn$(i), k, 1)) > 0 THEN good = 0: EXIT FOR
    NEXT
    IF good THEN goodCt = goodCt + 1: m$(goodCt) = tn$(j)
  NEXT
  IF goodCt > 1 THEN
    PRINT tn$(i),
    FOR j = 1 TO goodCt
      PRINT m$(j),
    NEXT
    PRINT
  END IF
NEXT i

Adapted from Enigma No. 1510, "Triangular threesome", by Richard England, New Scientist, 6 September 2008.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2008-12-27 06:19:48
SolutionSolutionDej Mar2008-10-22 06:50:50
SolutionDjck is between his friendsAdy TZIDON2008-10-21 20:09:00
No peaking...ed bottemiller2008-10-21 12:45:28
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 (4)
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