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Mensa IQ Cube, Dice and Paper Folding Flashcards

7 cards from real MENSA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Mensa IQ Cube, Dice and Paper Folding flashcards as text

  1. In a standard die, the number 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4. A die shows 5 on top. The sum of the five visible faces (top + four sides) is:

    Answer: 15

    Total of all faces = 21; the hidden bottom face opposite 5 is 6; so the 5 visible faces sum to 21 - 6 = 15.

  2. A square paper is folded so the bottom-left corner touches the top-right corner (diagonal fold). A hole is punched in the top-left corner of the folded triangle. When unfolded, how many holes are there and where?

    Answer: 2 holes — one at top-left and one at bottom-right of the paper

    Folding bottom-left to top-right folds along the other diagonal; the top-left corner of the folded shape corresponds to the original top-left and its mirror — punching there creates 2 holes at top-left and bottom-right.

  3. How many unit cubes in a 4×4×4 cube have exactly 1 painted face (assuming all outer surfaces are painted)?

    Answer: 24

    1-face cubes are the center squares of each face: each face of a 4×4×4 cube has a 2×2 region of face-only pieces = 4 per face × 6 faces = 24.

  4. A die is standing with 3 facing up and 6 facing the observer. It rolls once to the right (eastward tilt 90°). What now faces the observer?

    Answer: 6

    Rolling east tilts the die around the north-south axis; the front face (6, facing the observer) does not change — 6 still faces the observer.

  5. A net consists of 2 rows of 3 squares (2×3 grid). Which statement is true?

    Answer: This net cannot fold into a cube because two faces would overlap

    A 2×3 grid of 6 equal squares cannot fold into a cube — two faces inevitably overlap, making it an invalid cube net.

  6. A square piece of paper has a hole already punched in the upper-right quadrant. The paper is then folded in half vertically (right side onto left side). How many holes are visible in the folded paper?

    Answer: 2

    Folding the right half onto the left brings the original hole (upper-right) directly over the upper-left quadrant; both layers have the hole, so 2 holes are visible (stacked).

  7. Five dice are lined up in a row. The sum of all top-facing values is 23. What is the sum of all bottom-facing values?

    Answer: 35

    Each die's top and bottom faces sum to 7; with 5 dice, top+bottom total = 5×7 = 35; top faces sum to 23, so bottom faces sum to 35 − 23 = 12.