Abner challenges Benny to find out his secret number. On being requested by Benny for some clues, Abner says:

1. It is a 4-digit number.
2. The thousands digit is precisely 5 less than one-sixth of the number formed by the concatenation of its hundreds and tens digit (from left to right).
3. The hundreds digit is precisely 1.8 more than 1/40 of the number formed by the concatenation of its tens and units digits (from left to right).
4. Its tens digit is precisely 2 less than 5/4 times the units digit.

Determine Abner's secret number from the above-mentioned statements.

Refer to the clues as 1,2,3,4.
From clue 3:  CD/40 ends in .2  so CD is either 08, 48, 88; D = 8
From clue 3:  B = 1.8 + CD/40 which makes B:  {2,3,4} for C values of {0,4,8}
From clue 4: C = 8 therefore BCD is 488
From clue 2: 6 divides BC, with BC=48; so A = 8 - 5 = 3

ABCD is 3488


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for a in range(10):
    for b in range(10):
        for c in range(10):
            for d in range(10):
                bc = int(str(b)+str(c))
                cd = int(str(c)+str(d))
                if a + 5 == bc/6:
                    if b - 1.8 == cd/40:
                        if c + 2 == 5*d/4:
                            print(a,b,c,d)

Posted by Larry on 2023-04-07 08:02:23