School-Safe Puzzle Games

A Glorious Game

football brain teaser

Here’s a classic brain teaser: “At the close of last season, of the footballers of my acquaintance four had broken their left arm, five had broken their right arm, two had the right arm sound, and three had sound left arms.”

Can you discover from that statement what is the smallest number of players that the speaker could be acquainted with?

answers to be revealed in 2 days.

21 Comments to “A Glorious Game”

  1. ana margarita | Guest

    there are seven players. maybe.

  2. jason | Guest

    i have come up with seven….two being completely healthy, with 4 having both arms broken, and one having the right arm broken.

  3. andy | Guest

    one is the answer in respect of the smallest number of acquaintances.

  4. suineg | Guest

    I think one answer can be this:

    first you start by “minimal” number of players, you have 4 groups:
    1) with broken right arm–> 5 (A)
    2) with broken left arm –> 4 (B)
    3) with right arm sound–> 2 (C)
    4) with left arm sound–> 3 (D)
    note: the letters represent each group

    the “minimal” number of players is met when every player can be in as many groups he can be so, in conjunts is where the more unions exists So:
    1)the 2 of C exist in A,B,D–>so A(5-2=3) B(4-2=2) C(2-2=0) D(3-2=1)
    2)the 1 left in D exist in A,B–> so A (3-1=2) B(2-1=1)D(1-1=0)
    3)the 1 left in B exist in A–> so A( 2-1=1)B(1-1=0)
    4)The 1 left in A exist only in A(1-1=0)
    so the minimal number is 2+1+1+1= 5
    and the categorization is this:
    1) 2 have broken left and right arm and also have sound right and left arm
    2) 1 have left and right arm broken but only left arm sound
    3) 1 have left and right arm borken but neither arm sound
    4) 1 have only the right arm broken

  5. Alex | Guest

    4 broken left + 3 sound left = 7
    5 broken right + 2 sound right = 7

    Least number of players aquainted with speaker = 7

  6. Sven | Guest

    7 in the smallest number

    >Start with 4 players with both arms broken.
    so 4 left, 4 right broken arms.

    >Add 1 to have the additional right broken arm and 1 unbroken left arm.

    >Add 2 players with neither arm broken
    >4+1+2= 7

    So we have 4 broken left arms, 5 broken right arms, 2 unbroken right arms and 3 unbroken left arms. QED

  7. Jeff | Guest

    Fewest number of players would be 7. The number of broken left arms or broken right arms are not mutually exclusive. There could be 4 players with both arms broken, 1 with their right arm broken and 2 with neither arm broken. 4+2+1=7

  8. Will | Guest

    I figure: 7 people in total

    4 with R & L arms broken = 4 (L broken) & 4 (R Broken)
    1 with Right arm only broken = 1 (L is ok) & 1 (R Broken)
    2 with R& L arm ok = 2 (L ok) & 2 (R ok)

    7 = 4 (broken lefts), 5 (Broken Rights), 3 (ok Lefts), 2 (ok Rights)

  9. scott k | Guest

    7. just count total # of each arm is talked about

  10. Kevin from Bathurst | Guest


  11. Shawn | Guest

    7 total players

    4 with both left and right arms broken
    1 with only the right arm broken
    2 with no arms broken

  12. Tori | Guest

    7..? Seems too easy! What have I missed?

  13. Mark W | Guest

    Left arms: 4 broken, 3 ok
    Right arms: 5 broken, 2 ok

    I count 7 left arms and 7 right arms so that’s 7 people.

  14. suineg | Guest

    i have a question: the expression “sound(left or right) arm” means healty ( left or right) arms??

  15. suineg | Guest

    I used to believe that sound arm was something refering a luxation or a dislocation, thats why i thought that sound arm and broken arm were not mutually exclusive, but cool puzzle indded, i learn that sound arm means something close to healthy arm, and my answer in that case will be:
    1) 4 with both arms broken
    2) 1 with the right arm broken and the left ok (sound)
    3) 2 with the two arms ok (sound)
    4+1+2=7 the same answer that everyone post it above but me

  16. RK | Profile

    Hi Suineg-sorry didn’t answer you earlier; ‘sound arm’ meaning ‘healthy arm’ (intact)

  17. Tommy | Guest

    a lot of people are using
    4 with both broken
    1with right broken and left sound
    and 2 with both arms sound

    I just wanted to make sure that people know that there are also 2 other possible scenarios with 7 people.

    One being
    3 both broken
    2 left sound right broken
    1 left broken right sound
    and 1 both sound

  18. | Profile

    I think there is 7 people the person he knew.It was like this:

    1) 14 players in all
    2) 4 players had both arms injured
    3) 1 player with right arm broken and left sound
    4) 2 players with both arms sound

    IN ALL=7 players

  19. dezcifrando | Profile

    My answer is 5 players. Using the Venn diagram, you can easily figure it out. I agree with @suineg. You have to have in your mind that players can sound and also break both of their arms. You will need to make 3 Venn diagrams

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