# digit puzzle

What 5 digit number am I thinking of.

It has two prime digits.

Digit 3 is the highest digit.

Digit 2 is lowest digit.

Digit 1 is higher than the sum of digits 4 and 5.

Digit 5 is half of digit 4.

Digit 1 is one smaller than digit 3.

Digit 5 is between digit 2 and digit 1

There are no duplicates and the digit 0 does not appear.

Do not forget that 1 is not prime.

Answer: 71842

Solution:

a b c d e (digits of given number)

2 prime digits

9 >= c > a, d, e > b >= 1

a > d + e

e = d/2

a = c – 1

b < e = a+1 > a, e, 2e > b >= 1

a > 2e + e = 3e

e > b & b >= 1 => e >= 2

if e >= 3 then a > 3e >= 9, but a can’t be greater than 9 so e can’t be greater than or equal to 3, which means e = 2

=> d = 4, b = 1

e is prime, but b and d are not, which means that a or a+1 is prime

a+1 a 3e => a > 6,

so a can be 7 or 8, since 7 is only prime digit of digits 7, 8, 9 then a must be 7 and c = a+1 = 8

conclusion: a = 7, b = 1, c = 8, d = 4 and e = 2

number: 71842 (2 and 7 are prime, 8 is the highest digit, 1 is the lowest digit, 7 is higher than sum of 4 and 2, 2 is half of 4, 7 is smaller than 8, 2 id between 1 and 7)

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