i am a four -digit number with no two digits the same. my ones digit is twice my thousands digit and one less than my tens digit. my hundreds digit is the difference between my tens digit and my thousands digit. my thousands digit is an odd number less than 6.
what number am i?
i think i have posted it but i can't see it on the site
???
3426
let the number be abcd
given:
d=2a
d=c-1 ------>c=d+1
b=c-a
a<6 and odd, so a = 1,3,or5
no two digits are the same
rule out a=5 because then d=10, not possible
let a=1, then
d=2
c=3
b=2, but that would be two digits the same
let a=3, then d=6
c=7
b=4
the number is 3476
thanks
3476 makes sense!
3476
To solve this problem, we need to analyze the given conditions and find a four-digit number that satisfies all the conditions.
Let's break down the given conditions step by step:
1. "I am a four-digit number with no two digits the same."
This means that all four digits in the number must be different.
2. "My ones digit is twice my thousands digit and one less than my tens digit."
Let's represent the number as "abcd," where a is the thousands digit, b is the hundreds digit, c is the tens digit, and d is the ones digit.
From this condition, we know that d = 2a and d = c - 1.
3. "My hundreds digit is the difference between my tens digit and my thousands digit."
From this condition, we know that b = c - a.
4. "My thousands digit is an odd number less than 6."
This condition tells us that a can be either 1, 3, or 5.
Now let's go through each possible value for a and check if it satisfies all the conditions:
1. For a = 1:
- d = 2, c = 3, and b = 2.
But in this case, b is not equal to c - a, so it doesn't satisfy the conditions. Therefore, a = 1 is not valid.
2. For a = 3:
- d = 6, c = 7, and b = 4.
This satisfies all the conditions, as b = c - a and d = 2a. So, the number is 3476.
Therefore, the four-digit number that satisfies all the given conditions is 3476.