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
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
To find the number that matches all of these clues, we can break down each clue and determine the digit in each place value.
1. The digit in the thousands place is six times the digit in the tens place.
Let's represent the digit in the thousands place as A and the digit in the tens place as B. According to the clue, A = 6B.
2. The digit in the ones place is double the digit in the ten thousands place.
Represent the digit in the ones place as C and the digit in the ten thousands place as D. According to the clue, C = 2D.
3. The number has less hundreds than tens.
Let's represent the digit in the hundreds place as E and the digit in the tens place as B. According to the clue, E < B.
4. The number has six digits that are all different.
This means that all the digits A, B, C, D, E, and F (the digit in the hundred thousands place) are distinct.
5. The number has two hundred thousands.
Represent the digit in the hundred thousands place as F. According to the clue, F = 2.
Now, let's combine all the information we have gathered to find the number that satisfies all the clues.
Since F = 2, this means the digit in the hundred thousands place is 2.
Since A = 6B, and all the digits must be unique, B can only be 1. Therefore, the digit in the thousands place is 6.
Since C = 2D, and all the digits must be unique, D can only be 1. Therefore, the digit in the ten thousands place is 1.
Since E < B, and we already know B is 1, the digit in the hundreds place must be 0.
Now, we have the following digits: 2 (F), 0 (E), 1 (D), 1 (C), 1 (B), and 6 (A). Arranging them in descending order from left to right, we get the number 211602.
Therefore, the number that matches all of these clues is 211,602.