. There is a five digit number. It has two prime digits (1 is not a prime number). Third digit is the highest. Second digit is the lowest. First digit is one less than the third digit. The fifth digit is half of the fourth. The sum of 4th and 5th is less than the first. Find the number.
2006-07-31 07:17:19 · 10 answers · asked by navin s 1 in Science & Mathematics ➔ Mathematics
71842. good puzzle
2006-07-31 07:28:26 · answer #1 · answered by reiwo023-9085j 2 · 0⤊ 0⤋
Assuming number is abcde,
a <= 8 because it is one less than c, the largest number
d is even because e is 1/2 d
d + e = (3/2)d < a so d <= 5
This means that d = 0 or d = 2 or d = 4. But d cannot = 0 because then b could not be lowest, so d = 2 or 4.
Alright, we've reduced as much as possible. Let's assume d = 2 first. Then, we have e = 1 and a > d + e = 3 and b = 0.
So far, we have a0c21. We need one more prime digit. Assuming a is prime, it can equal 5, or 7 and we have:
50621
70821
Assuming c is prime, we have c = 5 or 7 as well (cannot be anything less or else a = c-1 < d + e = 3), we have
40521
60721
Alright, now we've exhausted it. Assume d = 4. Then, we have e = 2 and a > 6 and b < 2. So far, we have:
abc42
b cannot be prime so either a or c must be prime > 6. Well, c cannot be prime because then a = 6 is not > 6 so a must be prime = 7. For each of them, b can cycle between 0 and 1, so we have:
70842
71842
Thus, the answers are:
50621
70821
40521
60721
70842
71842
2006-07-31 07:34:19 · answer #2 · answered by tedjn 3 · 0⤊ 0⤋
It depends on whether 0 is allowed in the solution set, presumably as a non-prime if allowed. If allowed there are 3 answers 71842, 50621, and 70821.
The first seem to be the only solution without 0.
Solution by translation into algebraic statements, consolidating equalities where possible and then enumerating possibilities within the inequality restrictions.
2006-07-31 10:41:10 · answer #3 · answered by rhino9joe 5 · 0⤊ 0⤋
it's 71842:
7 and 2 are prime
8 is the highest
7 = 8 - 1
2 = 4/2
4 + 2 < 7
2006-07-31 07:31:27 · answer #4 · answered by Caroline I 2 · 0⤊ 0⤋
I think it is 71842. Its not 81942 because there is only one prime number(2). The only prime one digit numbers are 2,3,5, and 7. I just thought you should know.
2006-07-31 07:26:16 · answer #5 · answered by lasginny 2 · 0⤊ 0⤋
24817. LOL no one knows that the first digit is the one closest to the decimal point.
2006-07-31 07:47:15 · answer #6 · answered by DoctaB01 2 · 0⤊ 0⤋
71842
(Primes are 7, 2)
2006-07-31 07:35:10 · answer #7 · answered by aficionado 2 · 0⤊ 0⤋
So far, I can find more than one answer that fits your description.
70842
40521
There could be more...
2006-07-31 07:26:18 · answer #8 · answered by Sleeping Beauty 2 · 0⤊ 0⤋
81942
The above answer is probably wrong.. I never took math.
2006-07-31 07:24:21 · answer #9 · answered by Steven A 3 · 0⤊ 0⤋
i think it is 62741
2006-08-01 04:00:05 · answer #10 · answered by Anonymous · 0⤊ 0⤋