Enigmatic Code

Programming Enigma Puzzles

BrainTwister #13: Number Venns

1 Comment Posted by on 29 March 2024

From New Scientist #3484, 30th March 2024 [link] [link]

Numbers 1–30 are put in circle A if they are part of group A, in circle B if they belong to group B, in the intersection between if they are part of both A and B, or outside the circles if they don’t belong to either A or B. What are groups A and B for each diagram below (not all numbers have been placed yet)?

Only one of these diagrams can have another number added to the overlapping section using these rules.

Which diagram is it? And what is that number?

[braintwister13]

braintwister

One response to “BrainTwister #13: Number Venns”

  1. Jim Randell 29 March 2024 at 2:43 pm

    This is an exercise in spotting number sequences given examples and counterexamples.

    (If you don’t want to see my answers look away now…)

    Here are my hypotheses for the categories used in each diagram:

    Diagram 1:
    A = multiples of 3 = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
    B = multiples of 4 = {4, 8, 12, 16, 20, 24, 28}
    intersection = {12, 24}

    Diagram 2:
    A = primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
    B = even numbers = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
    intersection = {2}

    Diagram 3:
    A = triangular numbers = {1, 3, 6, 10, 15, 21, 28}
    B = square numbers = {1, 4, 9, 16, 25}
    intersection = {1}

    Only the first diagram can have a number added to the intersection, and that number is 24.

    Reply

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