Find a four digit number so that if a decimal point is placed between the hundreds digit, the resulting number is the average of the two-digit whole number on either side of the decimal point.

Question

anonymous · Answer

Consider this:$$
d_1d_2d_3d_4
$$

anonymous · Answer

IT is equal to: $$
d_110^4+d_210^2+d_310^1+d_410^0
$$

anonymous · Answer

$$
avg=\frac{(10d_1+d_2) +(10d_3+d_4)} 2
$$

anonymous · Answer

$$
avg=10d_1+d_2+\frac 1{10}d_3+\frac 1{100}d_4
$$

anonymous · Answer

That's a pretty damn good start.

anonymous · Answer

You could make it easier and just deal with two digits at a time rather than one digit at a time.

anonymous · Answer

$$
n=10d_1+d_2\
m=10d_3+d_4
$$

anonymous · Answer

$$
\frac{n+m}2=n+\frac m{100}
$$

anonymous · Answer

It will give you multiple solutions, but then you must bound them by $10\leq n,m\leq 99$