# 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)

### Your Answer

## More puzzles to try-

### 34+89=400 Matchstick Equation Puzzle

Correct the equation by moving one matchstick 34+89=400 As given in the matchstick equation (34+89=400) in the above diagram, move ...Read More »### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Dr. Willam and surgical gloves puzzle

Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### To which one will the needle touch 1 OR 2

In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Crossing the Bridge Puzzle (Bridge and torch problem)

A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »### Probability of having boy

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### How many times a day do all three hands of analog watch overlaps?

There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### Minimum number of persons needed to cross a Desert

In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »