Crack the Code: Escaping Dr. Schrödinger's Lair

You and your team of secret agents have stumbled into a trap set by the villainous Dr. Schrödinger, who plans to unleash an army of giant cats upon the city. Your mission: escape his underground lab by solving a perplexing numerical puzzle. Can you crack the code and save the day?

The Trap is Set

Dr. Schrödinger has disabled the control panel, leaving you with only three functional buttons: one that adds 5, one that adds 7, and one that takes the square root of the displayed number. Agent Epsilon has discovered the access code for the door: 2, 10, and 14. The challenge? Input these numbers in the correct sequence without triggering the panel's hidden traps.

The Rules of Engagement

• The display starts at zero.
• The target sequence is 2, 10, 14.
• The display cannot be reset.
• The room explodes if the same number appears more than once, the display shows a number greater than 60, or a non-whole number appears.

Time is running out. How will you navigate this numerical minefield?

Decoding the Escape Route

Your options are limited. The square root button can only be used on perfect squares. Let's analyze the possibilities:

• 4, 9, 16, 25, 36, and 49 are your potential square root triggers.

The Path to 2

Initially, reaching 4 or 16 seems ideal, as taking the square root once or twice would lead to 2. However, these numbers are unreachable directly from zero using only +5 and +7. The only viable option is 36.

1. Add 5, 7, 5, 7, 5, 7 (results in 36).
2. Take the square root (results in 6).
3. Add 5 twice (results in 16).
4. Take the square root twice (results in 2).

The Journey to 10

Directly adding to 10 from 2 is impossible without landing on another square number to utilize the square root function. Since 25 is unreachable from 2, you must aim for 9.

1. Add 7 (results in 9).
2. Take the square root (results in 3).
3. Add 7 (results in 10).

The Final Stretch: Reaching 14

To reach 14, consider the preceding number. It could be either 7 or 9. However, 9 has already been used, making 7 the only option. To get to 7, you must first reach 49.

1. Carefully add five 5s and two 7s, avoiding previously used numbers (results in 49).
2. Take the square root (results in 7).
3. Add 7 (results in 14).

Freedom!

By carefully threading the needle through this numerical maze, you input the code, the door swings open, and you escape Dr. Schrödinger's trap. Your problem-solving skills have saved the day, ensuring that Schrödinger's giant cat army remains a mere fantasy. As for the doctor himself, justice awaits!