School-Safe Puzzle Games

Scale Balance

Saw some comments show up recently on our first scale balance puzzle (hard!), which reminded me how long its been since we put one of these up. With that in mind:

How many triangles are need to balance scale 3?

feel free to submit your answers in the comment section below. Will unmask Thursday, thanks.

36 Comments to “Scale Balance”


  1. runninfool | Profile

    Comparing the first two pictures, 1 triangle = 2 circles = 4 squares since 1 circle = 2 squares.


    So, the last picture has 2 squares and 1 circle which can be translated to 4 squares.


    We need 1 triangle to balance this.


  2. bobg | Profile

    One Triange
    ______________
    X – Triange
    Y – Square
    Z – Circle


    1. X+2Y = 3Z
    2. X+Z = 6Y


    rearranged to find Triagle
    3. X=3Z-2Y
    4. X=6Y-Z


    Solve for Z
    5. 3Z-2y = 6Y-Z
    6. 4Z=8Y
    7. Z=2Y


    Check 7. with scale 1.
    1. X+2y = 3Z
    2. X = 2Z


    SO: X = 2Z= 4Y


    Therefore:
    Z+2y = ?
    Z + Z = ?
    2Z = X
    QED


  3. Ari | Profile

    The weights are: box 1, ball 2, triangle 4
    So one triangle should do the trick. Four boxes or 2 balls would work also.


  4. Norway | Profile

    Triangle= 4
    Square = 1
    Circle = 2


    So on the first balance scale its 6-6
    second is 6-6
    and on the third its 4-4


    So you will need a triangle on the third..


  5. gunturi | Profile

    It is one triangle
    From second balance one ball is equal to two squares.
    So, one Triangle is equal to four squares.
    For the third balance,
    the total weight in the left hand side is 4 squares which is equal to one triangle.


  6. vikram.mankal | Profile

    Let x = Green triangle
    y = Blue square
    z = Orange circle


    x + 2y = 3z -> (1)
    x + z = 6y -> (2)


    Eqn. (1) + (2) gives


    2x + 2y + z = 3z + 6y
    Therefore 2x = 2z + 4y
    Or x = z + 2y ( Dividing throughout by 2 )
    z + 2y is 1 Orange circle and 2 Blue squares
    So to balance this we need
    1 x or
    1 Green triangle


  7. T | Profile

    After reading how the previous ones were done I’ve come up with…


    In Balance 1, 1triangle (t) and 2 squares (2s) = 3circles (3c)


    In Balance 2, 1triange (1) and 1 circle(c) = 6squares (6s)


    and in Balance 3, 1 circle and 2 squares = x triangles (x(t))


    Re-arranging B1 and B2 to make t the subject…


    t = 3c – 2s and t = 6s – c
    .: 3c – 2s = 6s – c
    .: 4c = 8s
    .: c = 2s


    B3 can then be expressed as 2s + 2s = x(t)
    .: x(t) = 2c


    If 1 circle is equal to 2 squares you can take 1 circle from the right of B1 and 2 squares from the left of B1 and it will remain even.


    .: 1t = 2c (Or 1 triangle balances with 2 circles)


    Match this up with B3 and you get x = 1


    .: it will take 1 triangle to balance scale 3


    Testing with numbers… if 1t = 2c and 1c = 2s, then t and c must be even numbers. s=1, c=2 and t=4…


    Balance 1 is 4+1+1 = 2+2+2 (correct)
    Balance 2 is 4+2 = 1+1+1+1+1+1 (correct)
    Balance 3 is 2+1+1 = 4 (correct)


    Which confirms that 1 triangle will balance scale 3


  8. joe | Profile

    1 Triangle will balance the scale.


    Using the information given for Triangles (T), Squares (S) and Circles (C).
    First scale T + 2S = 3C
    Second one T + C = 6S which rearranging tells us that C=2S (one circle is 2 squares), and using that info and reinputing in the above that T=4S.
    On the left of the 3rd scale there is 1 C + 2 S or also equiv 2S + 2S =4 squares which we calculated was 1 triangle


  9. da Moose | Profile

    1 triangle = 2 circles = 4 squares


    Therefore, on balance no. 3, 1 circle + 2 squares = 1 triangle


  10. SolarFlare | Profile

    Only one green triangle is required on the rhs of balance 3. Explanation is as follows.


    Scale equations are (using the first letters of Green, Blue & Amber):
    G + 2B = 3A (B1)
    G + A = 6B (B2)
    2B + A = nG (B3)


    Rearranging:
    G = 3A – 2B (B1)
    G = 6B – A (B2)


    Subtracting these (B1 – B2) & rearranging:
    4A = 8B
    A = 2B


    We can now change the eqns B1 & B2 to eliminate A & express G in terms of B:
    3A – 2B = 6B – 2B = 4B = G (B1)
    6B – A = 6B – 2B = 4B = G (B2)
    (identical, as expected)


    Lhs of balance 3 becomes:
    2B + A = 2B + 2B = 4B


    And we know from above that:
    4B = G


    So only one G is required on the rhs of B3.


  11. foger1979 | Profile

    1 triangle


  12. GreekMind | Profile

    triangle = t
    square = s
    circle = c
    1t + 2s = 3c
    1t + 1c = 6s
    1c + 2s = ??*t


    (1) => 1t + 2s = 3c => t = 3c – 2s (a)


    (2) => 1t + 1c = 6s (a),(2)=> 3c – 2s +1c = 6s => 4c = 8s


    so c = 2s (a) => t = 3c – 2s = 3*2s -2s = 4s


    (3) 1c + 2s = 2s + 2s = 4s
    and 1t = 4s


    so the solution is 1 triangle


  13. Kira | Profile

    I got one triangle to balance the circle and two squares


    t=triangle, s=square and c=circle


    so from scale 1 we get the formula t+2s=3c and from scale 2 we have t+c=6s. From there we make t the subject of both formulas and get (Scale 1) t=3c-2s and (Scale 2) t=6s-c


    joining these two equations i get
    3c-2s=6s-c
    3c+c=6s+2s
    4c=8s


    c= 2s and conversely s=c/2


    if you then resubstitute these into the orginal scale 1 and scale 2 formulas you get


    Scale 1


    t+2s=3c
    t+2s=3(2s)
    t+2s=6s
    t=4s or s=t/4


    Scale 2


    t+c=6s
    t+c=6(c/2)
    t+c=3c
    t=2c or c=t/2


    Scale 3 is c+2s, which is (in terms of t) = t/2+2(t/4)= t/2+t/2 = t


    I’m sure i could’ve simplified that, couldn’t I?


  14. ekphron | Profile

    2 squares equal 1 circle
    2 circles equal 1 triangle
    the answer —
    1 triangle is needed to balance scale 3


  15. aaronlau | Profile

    Adding scale 1 & 2:
    2 Triangles + 2 squares + 1 circle = 6 squares + 3 circles
    => 2 Triangles = 4 squares + 2 circles
    => 1 Triangle = 2 square + 1 circle ! Scale 3


  16. suineg | PUZZLE MASTER | Profile

    I this this can be an answer:
    From the first 2 scales: 1 circle= 2 squares;
    1 triangle= 4 squares–> 1 triangle= 2 circles


    So in the thid scale: 1 circle + 2 squares= 4 squares—–>
    1 triangle, that I think is the answer


  17. Birdieguy | Profile

    One triangle.. unless I made a mistake in my algebra


  18. jibbo | Profile

    1


    one ball equels 2 squares
    one triangle equels 4 squares
    therefore 2 squares and one ball(2 squares) equels one triangle


  19. Poynter-Jones | Profile

    I just did a quick trial and error with the sequences of shapes and came up with this code:


    2 Blue squares = 1 Orange circle
    2 Orange circles = 1 green triangle
    1 Green triangle = 4 Blue squares




    3.)
    2 blue squares = 1 orange circle;
    Which leaves two orange circles, which equal one green triangle.
    Therefore to balance the other side of the scale, place one green triangle.


  20. nitwit88 | Profile

    1 triangle.


    circles->c, triangles->t, and squares->s
    3c=1t+2s and c+t=6s. Combining these and removing t, we get that 8s=4c, or 2s=c so we can consider the left side of scale three to be two circles. Plugging that into t+2s=3c, we get t+c=3c, which yields t=2c. That’s exactly how much we have on the left, so one triangle will balance it out.


  21. LadyInsomnia | Profile

    One triangle is needed to balance scale 3.


    Start by adding two triangles to the left-hand side. Then we have a triangle-plus-circle set and a triangle-plus-two-squares set. From scale one, we can add three circles to the right-hand side; from scale two, we can add six squares to the right-hand side, so scale three is balanced. Next, “cancel out” one circle and two squares from both sides. We’re left with two triangles balancing two sets of circle-plus-two-squares. So one triangle balances one circle plus two squares.


  22. paprika60 | Profile

    Okay, I’ve come up with ..
    1Triangle=2 Circles
    1Square=.5Circles
    1Circle=2Squares
    1Triangle=4Squares


    So, 1 Triangle would balance?


  23. tad | Profile

    One Triangle.


    1T + 2S = 3C
    1T + 1C = 6S


    1C + 2S = 1T


  24. NyteAzul | Profile

    Only 1 Triangle.


    1T + 2S = 3C
    -1T + 6S = 1C
    8S = 4C => 2S = 1C


    1T + 1C = 6S => 1T = 4S


    2S + 1C = 1T


  25. hex | PUZZLE MASTER | Profile

    Scale 1: 2 x S + T = 3 x C
    Scale 2: T + C = 6 x S
    Solving for C and S wrt T:
    C=T/2
    S=T/4
    Scale 3: 2 x S + C = T/2 + T/2 = T
    So one triangle balances scale 3


  26. Shawn | PUZZLE GRANDMASTER | Profile

    1 triangle.


    1 triangle = 4 squares = 2 circles


  27. RK | Profile

    1 Triangle = Answer. LOTS of good explanations above for this one, check them out


  28. michaelc | Profile

    jasc,


    That’s a neat way to look at it!


    I got the same answer as you did, but had to do all the algebra with pencil and paper.


    I’ll have to look at simpler ways to do things in the future. A picture really says a 1,000 words! :)


  29. wdrudder | Profile

    One triangle. One triangle equals two circles, one circle equals two squares, one triangle equals four squares.


  30. neutrondisciple | Profile

    1st scale – 1triangle=2circles & 2squares=1circle
    2nd scale – 1triangle=4squares & 1circle=2squares
    3rd scale – 1circle=half a triangle & 2squares=half a triangle


    so my answer is, one!


  31. skyadz | Profile

    there is only one triangle needed to balance scale 3.
    1 circle = 2 square
    1 triangle = 2 circle = 4 square
    to confirm..
    T=triangle S=square C=circle


    @ scale1
    1T + 2S = 3 C
    subs. T=2C S=1C
    2C + 1C = 3C
    3C=3C
    balanced…..


    @ scale2
    1T + 1C = 6S
    subs. T=4S C=2S
    4S + 2S = 6S
    6S = 6S
    balanced…,


    @ scale3
    1C + 2S=?
    T=2C T=4S,therefore C=1/2T S=1/4T
    1(1/2)T + 2(1/4)T
    T=1
    to balanced scale 3 we need 1 triangle…,


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