Jon Besga

Jon Besga

Personal notes about science, math, business, and programming

27 Jun 2020

Algebra Gelfand - Problem 1

Several digits “8” are written and some “+” signs are inserted to get the sum 1000. Figure out how it is done.

In this case we can to get the number 1,000 adding only digits composed by the number 8.

For that to happen we can add 8 several times until we get a 0. And that will be after adding 8 five times

\begin{aligned} 8 \\
8 \\
8 \\
8 \\
8 \\
40 \end{aligned}

Now, we have 4 as carry, so we need to look for the sum of adding 8 that after adding 4 give us another 0. That will be adding two 8, to get 16 and adding the carry we get 20.

\begin{aligned} 88 \\
88 \\
8 \\
8 \\
8 \\
200 \end{aligned}

Same process, this time the carry is 2 and we only need one “8”.

\begin{aligned} 888 \\
88 \\
8 \\
8 \\
8 \\
1000 \end{aligned}

And we get \( 1,000 \) as we wanted.

Another way is adding “8” 125 times, but that’s not very interesting.