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 Ordinal Days (Posted on 2010-02-17)
If the days of the week are represented as follows:

```MO TU W TH F SA SU

and are numbered 1 to 7 as follows:

MO TU  W TH  F SA SU
1  2  3  4  5  6  7
```

assign to each letter a non-zero digit so that the numbers represented by the day abbreviations given are each divisible by the digit assigned to that day, but by no higher digit.

 Submitted by Charlie Rating: 2.5000 (2 votes) Solution: (Hide) ```MO TU W TH F SA SU 89 74 3 76 5 12 14 w = 3: f = 5 used(3) = 1: used(5) = 1 FOR m = 1 TO 9 IF used(m) = 0 THEN used(m) = 1 FOR o = 1 TO 9 IF used(o) = 0 THEN used(o) = 1 mo = m * 10 + o good = 1 FOR i = 2 TO 7 IF mo MOD i = 0 THEN good = 0: EXIT FOR NEXT i IF good THEN FOR t = 1 TO 9 IF used(t) = 0 THEN used(t) = 1 FOR u = 1 TO 9 IF used(u) = 0 THEN used(u) = 1 tu = t * 10 + u good = 1 FOR i = 3 TO 7 IF tu MOD i = 0 THEN good = 0: EXIT FOR NEXT i IF tu MOD 2 = 0 AND good = 1 THEN FOR h = 1 TO 9 IF used(h) = 0 THEN used(h) = 1 th = t * 10 + h good = 1 FOR i = 5 TO 9 IF th MOD i = 0 THEN good = 0: EXIT FOR NEXT i IF th MOD 4 = 0 AND good = 1 THEN FOR s = 1 TO 9 IF used(s) = 0 THEN used(s) = 1 FOR a = 1 TO 9 IF used(a) = 0 THEN used(a) = 1 sa = s * 10 + a good = 1 FOR i = 7 TO 9 IF sa MOD i = 0 THEN good = 0: EXIT FOR NEXT i IF sa MOD 6 = 0 AND good = 1 THEN su = s * 10 + u good = 1 FOR i = 8 TO 9 IF su MOD i = 0 THEN good = 0: EXIT FOR NEXT i IF su MOD 7 = 0 AND good = 1 THEN PRINT mo; tu; w; th; f; sa; su END IF used(a) = 0 END IF used(a) = 0 END IF NEXT used(s) = 0 END IF NEXT END IF used(h) = 0 END IF NEXT END IF used(u) = 0 END IF NEXT used(t) = 0 END IF NEXT END IF used(o) = 0 END IF NEXT used(m) = 0 END IF NEXT ``` Based upon Enigma No. 1575, "All our days", by Adrian Somerfield, New Scientist, 12 December 2009, page 28.

 Subject Author Date Solution Dej Mar 2010-02-18 03:40:26 re(2): SPOILER Ady TZIDON 2010-02-17 15:47:07 re: SPOILER Justin 2010-02-17 15:01:26 SPOILER Ady TZIDON 2010-02-17 13:49:51

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