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Homework Help: Math puzzle: combinations of digits

  1. Jan 17, 2017 #1
    • OP warned about not using the homework template
    My 10 year old daughter was given this maths puzzle and I'm sure to you guys it would be pretty easy.

    You have 5 numbers 1,2,3,4,5

    Ho many possible combinations are there possibe for 1 digit combos,2 digit combos, 3 digit combos, 4 digit combos, and 5 digit combos. The numbers cannot repeat at any time and you cannot have the reverse of the numbers also (e.g 345 and 543 as same 3 numbers used in this 3 digit combo.)

    For single digit combos there is onviously only 5 combos 1-5 (5)
    For 5 digit combos there is only one combination 1-5 (1) as any other combo still uses the same 5 numbers
    I thought using 5*4*3*2*1 / 4+3+2+1 = (12) would be the correct answer for the 4 digit combos
    and that 5*4*3*2*1 / 3 +2 +1 = (20) would be correct for 3 digit combos and that 5*4*3*2*1 / 2+1 = (40) for 2 digit combos.

    So total combos 5 + 40 + 20 + 12 + 1 = 78 possible combos would be correct but it's not.

    What is the correct answer and can you explain how it is done.

    Thanks in advance
  2. jcsd
  3. Jan 17, 2017 #2


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    Staff: Mentor

    She should start by listing all possibilities for 2 digits (including reversals), then excluding reversals, and try to deduce a pattern from that.
  4. Jan 17, 2017 #3


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    Science Advisor
    Homework Helper
    Gold Member

    For 4-digit combos, every combo is defined by the number missing. So, there are not 12 of those.
  5. Jan 17, 2017 #4
  6. Jan 17, 2017 #5


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    Staff: Mentor

    You really think your daughter should only care about the numerical answer?
  7. Jan 18, 2017 #6
    The link that I included on my previous post showed the formula and how it works and the proof. Do you really think a maths teacher would allow a child just come up with a numerical answer anyway? Thanks for taking the time to reply.Take care.
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