A computer science problem by Thành Đạt Lê

0 0 0 0 × 3 = 0 0 0 0 0 \boxed{\phantom0}\ \boxed{\phantom0}\ \boxed{\phantom0}\ \boxed{\phantom0} \times 3 = \boxed{\phantom0}\ \boxed{\phantom0}\ \boxed{\phantom0}\ \boxed{\phantom0}\ \boxed{\phantom0}

Can we fill in the boxes with distinct digits so that the equation is satisfied?


Clarification: The above equation represents a 4-digit number multiplied by 3 to produce a 5-digit number, so the leftmost box is non-zero on either side.

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1 solution

Daniel Branscombe
Aug 15, 2017

There are 15 possible solutions:

4609 3 = 13827 4609*3=13827

5683 3 = 17049 5683*3=17049

5694 3 = 17082 5694*3=17082

5823 3 = 17469 5823*3=17469

5832 3 = 17496 5832*3=17496

5934 3 = 17802 5934*3=17802

6358 3 = 19074 6358*3=19074

6819 3 = 20457 6819*3=20457

6839 3 = 20517 6839*3=20517

6918 3 = 20754 6918*3=20754

8169 3 = 24507 8169*3=24507

8369 3 = 25107 8369*3=25107

9046 3 = 27138 9046*3=27138

9136 3 = 27408 9136*3=27408

9168 3 = 27504 9168*3=27504

Please tell the methods

Aditi Parmar - 3 years, 9 months ago

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exhaustive search, there is a very small number of possible values for the 4-digit number, so it was a simple matter of checking which ones resulted in a valid solution. Namely there are 9 9 8*7=4356 possible values for the 4-digit number.

Daniel Branscombe - 3 years, 9 months ago

So is this more of a Computer Science problem? Or is there a direct way to arrive at a solution?

Geoff Pilling - 3 years, 9 months ago

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I think it's CS, I've converted it. If I saw an elegant approach, then I'll convert it back.

Pi Han Goh - 3 years, 9 months ago

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I don't know, if I asked how many possible solutions are there, it's definitely computer science. This problem were asked for 5th graders. A kid handed the paper to me and said: "Could you solve this for me? I have to go to school. I will give you candies after school." How cute!

Thành Đạt Lê - 3 years, 9 months ago

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