Claude 3 Opus Riddles

How well does Claude 3 Opus solve riddles
Reasoning
Claude 3 Opus
Author

Jason Saito

Published

April 2, 2024

Introduction

I wanted to continue exploring the reasoning abilities of LLMs specifically in terms of its logical reasoning skills. I also wanted to interact more with Claude’s OPUS 3 model. I found these riddles and the match riddles online.

Riddle 1: Using only addition, add eight 8s to get the number 1,000.

Response

Here’s how you can add eight 8’s to get 1,000 using only addition:

888 + 88 + 8 + 8 + 8 = 1,000

The process: 1. 888 is the largest number that can be formed using the digit 8 three times. 2. 88 is the largest number that can be formed using the remaining two 8’s. 3. We are left with three more 8’s, which are added as single digits.

Thus, 888 + 88 + 8 + 8 + 8 = 1,000.

Thoughts

This is correct! This problem is similar to the match riddles that I used in an earlier blog post. I was suprised that the OPUS model was able to solve the riddle correctly and very quickly.

Riddle 2: A 300 ft. train is travelling 300 ft. per minute must travel through a 300 ft. long tunnel. How long will it take the train to travel through the tunnel?

Response

Okay, let’s approach this step by step:

  1. Understand the given information:
    • The train is 300 feet long.
    • The train is traveling at a speed of 300 feet per minute.
    • The tunnel is 300 feet long.
  2. Visualize the problem:
    • The train needs to travel its own length plus the length of the tunnel to completely pass through the tunnel.
    • Total distance to travel = Length of the train + Length of the tunnel
    • Total distance to travel = 300 feet + 300 feet = 600 feet
  3. Calculate the time taken:
    • Speed of the train = 300 feet per minute
    • Distance to travel = 600 feet
    • Time = Distance ÷ Speed
    • Time = 600 feet ÷ 300 feet per minute
    • Time = 2 minutes

Therefore, it will take the train 2 minutes to completely travel through the tunnel.

Thoughts

This is also correct! I like how the response was broken down into various steps and explained at each step. Overall, I’m very impressed by this Opus model. Given that the model was doing really well with these word riddles, I wanted to challenge it with match riddles again.

Riddle 3: Match Riddles

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Response:

To solve the mathematical equation shown in matchsticks, I would move the single vertical matchstick from the first equation (which appears to represent an addition operation) and place it next to the second equation. This would transform the second equation from an incorrect representation of 11 - 1 = 2 into a correct representation of 11 - 1 = 10.

Thoughts:

This is incorrect! I am not suprised, it seems like all models struggle with these match riddles and often get confused with what I’m asking it. I decided to go back to strictly word riddles and found a question from the AMC 10 (an exam that tests math and reasoning skills).

Riddle 4: AMC Question

Six regular hexagonal blocks of side length 1 unit are arranged inside a regular hexagonal frame. Each block lies along an inside edge of the frame and is aligned with two other blocks, as shown in the figure below. The distance from any corner of the frame to the nearest vertex of a block is 3 / 7 unit. What is the area of the region inside the frame not occupied by the blocks?

Response

The response was close to being right until the fifth step when it found a negative area and crashed.

Conclusion

Overall I am pretty happy with OPUS 3’s performance. It did very well with the initial easier riddles but struggled with the visual and more difficult riddles.