BluBridge - An Aspiring LLM Research Lab

1.

Four friends – A, B, C, and D – are seated around a circular table. It is known that A sits immediately to the left of B, and D sits directly opposite A. If B is at the north position, in which position is D seated?

a) South b) East c) West d) North

2.

Decode the following substitution cipher where each letter is replaced by the letter two positions later in the alphabet (wrap around from Z to A):

“JGNNQ”
What is the decoded word?

3.

In a cross pattern, the four corners are: top-left = 3, top-right = 7, bottom-left = 5, and bottom- right is unknown. The center number is 6, which is the average of the four corners. Find the missing number.

4.

5, 12, 25, 52, 105, ?

5.

You are given 8 coins, one of which is counterfeit and weighs slightly less than the others. Devise a strategy using only 2 weighings on a balance scale to identify the counterfeit coin. Explain your reasoning.

6.

Triangle (3 sides), Hexagon (6 sides), Pentagon (5 sides), Octagon (8 sides), Heptagon (7 sides), ?

7.

In this analogy,

8.

Consider the series of letter pairs: AB, BC, EF, GH, KL, … What is the next pair in the series?

9.

A large cube is painted blue on all its faces and then evenly cut into 27 smaller cubes (arranged 3×3×3). How many of these smaller cubes have no paint on them?

10.

What is the next letter in the sequence: J, F, M, A, M, J, J, A, S, O, ?

11.

Which two‑digit number, when rotated 180° on a seven‑segment display, yields a different valid two‑digit number?

a) 69 b) 96 c) 11 d) 88

12.

In a coded sequence, each letter of the word LOGIC is shifted forward by 2 positions in the alphabet. What is the resulting code?

13.

Three boxes are labeled “Apples,” “Oranges,” and “Apples & Oranges.” Each label is wrong. By selecting one fruit from a single box, determine the true contents of all three boxes.

14.

In a 4×4 grid, each cell’s value equals the sum of its row and column indices (indices start at 1). If one cell in row 3, column 4 is unknown, what is its value?

15.

Which of the lower boxes best completes the series on the top?

16.

Given 12 identical coins (one of which is counterfeit and slightly heavier), determine the minimum number of weighings on a balance scale required to always find the heavier coin.

17.

A puzzle shows a cyclic color transformation for a shape: red becomes blue, blue becomes green, and green becomes red. If a shape starts as red and undergoes 6 consecutive color changes, what is its final color?

a) Red b) Blue c) Green d) Indeterminate

18.

Riddle: “I am the invisible thread connecting your past to your future. I have no form, yet I build the stories of your life. I can be forgotten but never truly lost.” What am I?

19.

What is the missing number in this series?

1 3 9 ___ 81 243

20.

Given the statements “Every scientist is curious” and “Some engineers are scientists,” which of the following conclusions is logically valid?

a) Some engineers are curious. b) All engineers are curious.
c) All scientists are engineers. d) No conclusion can be drawn.