We are looking for the smallest natural number n with the property that both the digit sum Q(n) of the number n and the digit sum Q(n + 1) of the successor of n are divisible by 5.

During a birthday party, the birthday child realizes: In 1968, I was the same age as the sum of the digits of my birth year. How old will I be now at the end of 2025?

(Please no AI solution)

In the decimal system, specify the smallest natural number k that begins with the digit 7 and has the following additional property:
If you delete the first digit 7 and write it at the end, the newly created number z = (1/3)*k.

I would like to experiment with error estimation in the symbolic solution of ordinary differential equations. I've written a simple example in the attached file. I would now like to plot both the left side of the ODE and the solution y(x) together in the same coordinate system. I can't do this, and I'm asking for help. How can the cumbersome numerical terms in the solution y(x) be converted to floating-point numbers?

As I said, this is a recreational experiment ;-) .DGL_test.mw

Download DGL_test.mw

...but it's easily solvable with the help of a trick. My main concern is the path to the solution for the attached Diophantine equation. I was able to solve the problem both with pen and paper and then in Maple. There's certainly a more elegant way. I'm particularly interested in a special Maple command. However, I don't want to ask for it here yet, as it would give a hint of the trick and spoil the fun of solving the puzzle.

Download Diophant.mw