# Enigmatic Code

Programming Enigma Puzzles

## Enigma 1575: All our days

From New Scientist #2738, 12th December 2009 [link]

I have written the days of the week with their ordinal numbers as shown above.

Letters being consistently replaced by non-zero digits, each day is divisible by its own ordinal number (and by no higher digit).

What is the FAMOUS number?

[enigma1575]

### One response to “Enigma 1575: All our days”

1. jimrandell 12 February 2012 at 10:53 pm

The following Python program runs in 41ms.

```from itertools import permutations

# there is only one possibility for each of F, W
(F, W) = (5, 3)

# U, H, A are even
for (U, H, A) in permutations((2, 4, 6, 8), 3):

d1 = set(range(1, 10)).difference((F, W, U, H, A))
for (T, S) in permutations(d1, 2):
(TU, TH) = (10*T + U, 10*T + H)
if TH % 4 or not all(TH % n for n in range(5, 10)): continue
if not all(TU % n for n in range(3, 10)): continue
(SU, SA) = (10*S + U, 10*S + A)
if SU % 7 or not all(SU % n for n in range(8, 10)): continue
if SA % 6 or not all(SA % n for n in range(7, 10)): continue

d2 = d1.difference((T, S))
for (M, O) in permutations(d2, 2):
MO = 10*M + O
if not all(MO % n for n in range(2, 10)): continue

print("FAMOUS", "=", F, A, M, O, U, S, sep='')
```

Solution: FAMOUS = 528941.