1
$\begingroup$

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.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

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

Improve this answer
$\endgroup$
2
  • $\begingroup$ 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. $\endgroup$
    – Will.Octagon.Gibson
    Commented Sep 13, 2022 at 19:11
  • $\begingroup$ Fixed, and added the appropriate explanation. $\endgroup$
    – AxiomaticSystem
    Commented Sep 13, 2022 at 20:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.