what is the four digit number which satisfies these conditions;

The last digit is twice the first digit.
The second digit is twice the third digit.
The sum of the first and last digits is twice the third digit.

a b c d

d = 2 a

b = 2 c

a+d = 2 c

----------------------
a = 2 c - d = 2 c - 2 a
so
3 a = 2 c
hmmmm
if c is 1, nope
need common multiple for integer like
3 a = 6
2 c = 6
looks like a = 2 and c = 3
so far:
2 b 3 d
but d = 2 a
2 b 3 4
b = 2 c so
2 6 3 4

2634

thank you verymuch. But how 3a=6?

I needed a common multiple of 2 and 3

that is 6
we are not doing fractions here, just integers

ok thank you. God blss you

To find the four-digit number that satisfies the given conditions, we can break it down step by step:

Condition 1: The last digit is twice the first digit.
Let's represent the four-digit number as ABCD, where A is the thousands digit, B is the hundreds digit, C is the tens digit, and D is the units digit. From the first condition, we know that D = 2A.

Condition 2: The second digit is twice the third digit.
This condition tells us that B = 2C.

Condition 3: The sum of the first and last digits is twice the third digit.
We are given that A + D = 2C.

By combining all three conditions, we can solve for the values of A, B, C, and D. Let's substitute the known relationships from the first two conditions into the third condition:

A + D = 2C
A + 2A = 2C (substituting D with 2A)
3A = 2C

Now, let's substitute the known relationship from the second condition into the equation above:

3A = 2B
3A = 2(2C) (substituting B with 2C)
3A = 4C

We now have two equations:

3A = 4C ---(1)
3A = 2C ---(2)

By equating the right sides of these two equations, we can solve for C:

4C = 2C (from equation 1 and 2)
2C = 0
C = 0

Now that we know the value of C, we can substitute it back into either equation (1) or (2) to find the value of A:

3A = 2C
3A = 2(0) (substituting C with 0)
3A = 0

In this case, A must also be zero.

From condition 1, we know that D = 2A, which means D = 2(0) = 0.

Finally, from condition 2, we know that B = 2C, which means B = 2(0) = 0.

Therefore, the four-digit number that satisfies all the given conditions is 0000.