a maths puzzle?

Question

.There is a five-digit no. following conditions were given about the same number.
-> There are two prime nos in that number.
-> No duplicates are there.
-> Digit 3 is the highest.
-> Digit 2 is the lowest.
-> Digit 5 is between digit 2 and digit 1 and is half of digit 4.
-> Digit 1 is one less than digit 3 and is greater than sum of digit 4 and digit 5.
Find the number.(Don't take 1 as prime no.) It was given there in the paper.

Answer 1

71842

Answer 2

This question is identical to the one you gave right before. The rephrased and added conditions simplify into the same ones, thus my answers are the same.

Repeat of my answer.
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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
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@Iluvharrypotter_tonima,

Digit 4 does have to be even, as you correctly noticed, but D4 + D5 < D1!

Check your answers. Many of them have more than 2 prime numbers.

@wishiwerewest,

Even without the stipulation in the problem that 1 is not to be considered prime, 1 should never be considered prime anyways. In any case, all prime numbers have 2 factors, 1 and itself. 1 is the exception in that it only has 1 factor! It's neither prime nor composite.

@DutchProf,

Isn't 0 a digit as well :-D

Answer 3

NOTE: 1 IS NOT A PRIME NUMBER.
Not only we algebraists say so... the problem does too :)

If #5 is half of #4, then #4 is not a prime number.
If moreover #1 > #4 + #5, then #5 = 1 or 2.
If #5 is between #2 and #1, it must be 2, and either #1 or #2 is equal to 1.
Since #2 is the lowest, it must be equal to 1.
Because #5 = 2 is half of #4, we know #4 = 4; their sum is 6, so #1 > 6.
For #3 to be the largest it must be more than #1, so #3 is 8 or 9.

Thus far we have #1 = 7 or 8; #2 = 1; #3 = 8 or 9; #4 = 4; #5 = 2.
Prime numbers can help us resolve #1. Because 2 is the only other prime number possible, #1 must be equal to 7; hence #3 = 8.

The number is 71842.

Answer 4

THere is a half of digit 4, whic hmeans its an even number. So it is either 2,4,6 or 8
which would make digit 5 either 1,2 3 or 4
which would make digit 2 and 1 either 0 and 2, 1 and 3, 2 and 4 or 3 and 5
which would make digit 3 either 3, 4, 5 or 6
so the possible numbers are: 20321, 31442, 42563 or 53684
what am I doing wrong?

Answer 5

71842 is not correct as it has three prime numbers in it (1, 2 and 7). The problem indicates only two prime numbers are in the answer.

Answer 6

that confused the heck out of me but the girl that answered before me is right