Question

WHAT NUMBER MATCHES ALL OF THESE CLUES.
The digit in my thousands place is six times the digit in my tens place
The digit in my ones place is double the digit in my ten thousands place
I have less hundreds than I have tens
I have six digits that are all different
I have two hundred thousands

Answer 1

Your number is:

a ∙ 100 000 + b ∙ 10 000 + c ∙ 1 000 + d ∙ 100 + e ∙ 10 + f

Numbers a , b , c , d , e and f must be 0 to 9.


I have two hundred thousands:

a = 2

The digit in my thousands place is six times the digit in my tens place:

c = 6 e

c = 6 , e = 1

because 6 ∙ 1 = 6 , 6 ∙ 2 = 12 , 12 is greater than 9


I have less hundreds than I have tens:

d < e

d < 1

d = 0


The digit in my ones place is double the digit in my ten thousands place:

f = 2 b

I have six digits that are all different.

b cannot be 1 because 2 ∙ 1 = 2

a = 2 so 2 already exists

b cannot be 2 because f = 2 b = 2 ∙ 2

All numbers must be different so two numbers 2 cannot be in the required number.

b cannot be 3 because 2 ∙ 3 = 6

c = 6 so 6 already exists

b can be 4 because 2 ∙ 4 = 8

b cannot be 5 because 2 ∙ 5 = 10 , 10 is greater than 9

So:

b = 4

f = 2 b

f = 2 ∙ 4

f = 8

Your number:

246018