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The following problem was given in the Eureka journal (October 1963/University of Cambridge). This problem can be solved by hand without computers. There is a unique solution. Have fun solving!

Fill in the asterisks with digits other than three to make a correct division. You can assume that all leading digits are non-zero.

      *3*
   ------
*3*)3***3
    ***
    ---
     ***
     ***
     ---
      **3
      **3
      ---
        O

I would like to acknowledge Beastly Gerbil’s help in formatting this long division.

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1 Answer 1

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Good introductory puzzle! The answer is

32943 / 139 = 237.

Why?

Consider the final step in the division. The last digits have to multiply to something ending in 3 - this can be achieved via 1×3 or 7×9, but since unknown digits are not 3, the latter pair must be correct. Now the 9 cannot be in the quotient or the final product would be 9×137, a 4-digit number. The dividend must be 139, since 7×239 is also a 4-digit number, and the quotient must begin with 2 for the first subtraction to remove the initial 3, which makes it 237.

Obligatory image, showing that none of the other hidden digits are 3:

enter image description here

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  • $\begingroup$ What you refer to as the dividend is actually the quotient. The five-digit number 3***3 is the dividend. Can you please explain why the first digit of the quotient can’t be one. $\endgroup$ Sep 13, 2022 at 19:11
  • $\begingroup$ Fixed, and added the appropriate explanation. $\endgroup$ Sep 13, 2022 at 20:49

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