### Brain Teasers

# Find the Number

The number has 5 digits.

a: the first and the third digit are the same, all others are different.

b: the highest digit is 7 and the lowest is 1.

c: the third digit is twice as much as the fourth.

d: the second digit is higher than the fifth.

e: the sum of the five digits is 23.

What is the number?

a: the first and the third digit are the same, all others are different.

b: the highest digit is 7 and the lowest is 1.

c: the third digit is twice as much as the fourth.

d: the second digit is higher than the fifth.

e: the sum of the five digits is 23.

What is the number?

### Answer

67631Because of 'a' and 'c' there are three possibilities:

2-21- (with 7 and 6 we only get 18)

4-42- (with 7 and 1 (b) we get 18)

6-63- (b says we need a 7 and a 1, and d shows the position.)

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## Comments

very nice logic

I did it differently. The three unknown digits total 15. The repeated digit must be even, so it can't be seven. There's only one set of three numbers with two even numbers less than seven that total 15: 6,6,3. Assigning the numbers was simple after that.

@javaguru: 6,5,4 is another set of three numbers (two being even) whose sum is 15. Not that it works for this teaser since the two even numbers are not the same; just saying.

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