School-Safe Puzzle Games

The March is On!

army march math puzzle

A group of warriors was marching in regular column, with five men more in depth than in front. When the foe came in sight the front was increased by 845 men, and the whole was thus drawn up in five lines.

How many men were there in all?

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11 Comments to “The March is On!”


  1. Shawn | PUZZLE GRANDMASTER | Profile

    4550


  2. MarkS | Profile

    If I understand the question then with x = number of columns so
    number of men is x(x+5) from the first part. And from the
    second part, the number of men is 5(x+845). Equating the two
    gives x**2 = 4225, so x = 65 and number of men is 4550.


  3. Bobo The Bear | PUZZLE MASTER | Profile

    Took a while to decipher the wording on this one (I kept thinking 845 men joined the original company, rether than just a reformation of the troops).


    Original formation: X wide by (X+5) deep.
    New formation: (X+845) wide by 5 deep.
    Equation: X(X+5)=5(X+845)
    Solution: X=65
    Original formation: 65 by 70 = 4550 men.
    New formation: 910 by 5 = 4550 men.


  4. Hex | PUZZLE MASTER | Profile

    D: depth
    F: front
    T: total


    D=F+5
    T=FxD=Fx(F+5)


    F’=F+845
    D’=5
    T=5x(F+845)


    Fx(F+5)=5x(F+845)
    F2 + 5F = 5F + 5×845
    F=sqrt(5×845)=65
    D=F+5=65+5=70
    T=FxD=65×70=4550 men


  5. suineg | PUZZLE MASTER | Profile

    Initially you have x rows and x+5 columns, when the foe appeared you then have x + 845 rows and 5 columns so you have to combine this equations:
    x(x+5) = (x +845)5 — then you have x = 65 and in total you would have 65X70= 4550 men
    verification: 65 + 845 = 910 X 5= 4550


    Cool man!, I am kind of depressed cause I just took the GRE and score 790 in the quantitative section!!!! so much practice for nothing, Dont bother asking for the verbal score, I should ask Shawn for those weird looking words: babble … and so forth jajajaja so gone are my MIT admissions hopes but cool!!


  6. RK | Founder | Profile

    Very good, 4550 is the answer.


    Suineg, isn’t a 790 an almost perfect score?!


  7. suineg | PUZZLE MASTER | Profile

    yes RK the ceiling is 800 but 790 is not enough for MIT standars for scholarships I gonna try anyway but I should have get the 800, It is not really that hard but well nothing to do now


  8. Chris Edwards | Profile

    4550. Took a lot longer to figure out what my password was! Not much of a challenge… that is, if I have the correct answer!


  9. Chris Edwards | Profile

    well, I guess I do. That was a bit grade school-ish, though I’ve always loved word problems. Also never able 2 fathom why so many peeps can’t figure out how to set em up! More math problems, pleeeze!


    What R U if U R not part of the solution? U’r part of the precipitate! hahahaha!


  10. Hendy | Profile

    If ur not part of the precipate ur part of the solvent.


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