 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  One More Factor, Please (Posted on 2008-03-23) Four three-digit numbers are in arithmetic progression, and the number of factors of each is also in arithmetic progression. In fact that second arithmetic progression has a constant difference of 1, so that each successive number in the original arithmetic progression has one more factor than the number before it.

Note: These are not the prime factors of the numbers, but rather any factor, including the number itself and 1, so, for example, 46 has four factors (1, 2, 23 and 46), as does 8 (1, 2, 4 and 8).

What is the original arithmetic progression of three-digit numbers?

 Submitted by Charlie Rating: 3.3333 (3 votes) Solution: (Hide) ```number factors 229 2 (1, 229) 361 3 (1, 19, 361) 493 4 (1, 17, 29, 493) 625 5 (1, 5, 25, 125, 625) ``` The numbers being factored differ by 132 from one to the next. ```DECLARE FUNCTION factors# (n#) DEFDBL A-Z CLS DIM nfact(100 TO 999) FOR n = 100 TO 999 nfact(n) = factors(n) NEXT FOR strt = 100 TO 999 - 3 FOR diff = 1 TO 333 IF strt + 3 * diff > 999 THEN EXIT FOR dif2 = nfact(strt + diff) - nfact(strt) IF dif2 = 1 THEN IF nfact(strt + 2 * diff) = nfact(strt + diff) + dif2 THEN IF nfact(strt + 3 * diff) = nfact(strt + 2 * diff) + dif2 THEN FOR i = strt TO strt + diff * 3 STEP diff PRINT i, nfact(i) NEXT PRINT : PRINT diff END IF END IF END IF NEXT NEXT FUNCTION factors (n) test = n: lim = INT(SQR(n) + .5) ct = 0 FOR i = 1 TO lim q = INT(test / i + .5) IF q * i = test THEN IF q = i THEN ct = ct + 1: ELSE ct = ct + 2 END IF NEXT factors = ct END FUNCTION ``` Based on Enigma No. 1479 by Richard England, New Scientist, 2 February 2008. Comments: ( You must be logged in to post comments.)
 Subject Author Date Answer K Sengupta 2008-12-31 00:39:16 re: Solution / method ==>>MY WAY Ady TZIDON 2008-03-24 20:43:13 Solution / method ed bottemiller 2008-03-24 15:19:59 Solution Dej Mar 2008-03-23 21:34:02 one solution xdog 2008-03-23 12:51:04 Please log in:

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