The Old Calculator has buttons that turn a number into a certain other number. This affects all numbers currently displayed on the calculator's screen. For example, the button "5->6" changes a 52 into a 62 and a 55 into a 66. There are ten essential buttons like this and each one is different. Here's a list of the buttons from left to right and from top to bottom

• 2->4
  
• 4->7
  
• 7->3
  
• 3->0
  
• 0->8
  
• 8->9
  
• 9->1
  
• 1->5
  
• 5->6
  
• 6->2

On top of that, there are keys for "Add 1" and "Subtract 1" as well as for adding and subtracting 10. You can also reverse the number shown on the calculator screen, for example turning a 41 into a 14.

If we arrange the list of main buttons into one string, we get the following:

To use this string to our advantage, we have to understand that some numbers need to be changed in certain ways to avoid mistakes. Let me give you an example.

• Starting Number: 74
  
• Target Number: 95
  
• We change the 7 into a 9 with 4 button presses.
  
• Number on screen: 94
  
• We want to change the 4 into a 5.

That's where the issue arises because while changing the 4 into a 5 the screen will be showing 99 after 5 button presses. If we would now continue in the string and press the "9->1" button, we would get an 11, not a 91, because all nines on screen are changed. This example shows how important it is, to make sure to change the numbers in the right order.

Here's an easy way to avoid this mistake:

• Reverse the number to get a 47.
  
• Change the 7 into a 5.
  
• Change the 4 into a 9.

I hope this was helpful to understand and beat the Old Calculator.