Solve the 5‑Digit Reverse‑Multiplication Puzzle with SQL Queries

A father encountered his third‑grade daughter's math problem: find a five‑digit number ABCDE such that ABCDE * 4 = EDCBA, with all digits distinct. Curious about solving it with code, he posted the challenge and invited the community to provide SQL solutions.

Solution by qingyun

This approach builds all permutations of five digits (0‑9) using a hierarchical query, filters out repetitions, constructs the number, and checks the multiplication condition.

with a as (select level-1 as x from dual connect by level <= 10)
select a.x*10000 + b.x*1000 + c.x*100 + d.x*10 + e.x as y
from a a, a b, a c, a d, a e
where a.x > 0
  and (a.x*10000 + b.x*1000 + c.x*100 + d.x*10 + e.x) * 4 =
      e.x*10000 + d.x*1000 + c.x*100 + b.x*10 + a.x
  and a.x <> b.x and a.x <> c.x and b.x <> c.x
  and a.x <> d.x and b.x <> d.x and c.x <> d.x
  and a.x <> e.x and b.x <> e.x and c.x <> e.x and d.x <> e.x;

Solution by regonly1

This method generates numbers of up to five digits, creates their reversed form, and filters those that satisfy the 4× relationship.

select * from (
  select level lvl,
         to_number(replace(sys_connect_by_path(l, ','), ',')) num,
         to_number(reverse(replace(sys_connect_by_path(l, ','), ','))) rnum
  from (select level-1 l from dual connect by level <= 10)
  connect by nocycle prior l <> l and level <= 5)
where num >= 10000
  and num < 100000
  and num * 4 = rnum;

Solution by hudingchen

A concise query that generates candidate numbers directly and checks the reverse‑multiply condition.

SELECT m.v
FROM (SELECT LEVEL*4 v FROM DUAL CONNECT BY LEVEL <= 99999/4) m
WHERE m.v >= 40000
  AND m.v = REVERSE(TO_CHAR(m.v)) * 4;

The query returns the unique solution 87912, confirming that 87912 * 4 = 21978, which is the reverse of the original number.

These examples illustrate how a seemingly pure‑math puzzle can be tackled with relational‑database techniques, turning a classroom exercise into an engaging coding challenge for developers.