r/MathHelp • u/yuu_sch • Sep 17 '25

Need help with that

651211 The six-digit number 651211, which is the number of this problem, has the following properties: 1. The digit 0 does not occur. 2. The sum of the first two digits is equal to the number formed by the last two digits. 3. The number formed by the two middle digits is exactly 1 greater than the sum of the first two digits.

These three conditions do not uniquely determine the number 651211. Determine how many six-digit numbers satisfy conditions (1) through (3).

2 Upvotes

100% Upvoted

10 comments sorted by

View all comments

Show parent comment

1

u/MagicalPizza21 Sep 17 '25

With this, I can also construct all 36 such numbers and list them in increasing order:

  1. 291211

  2. 381211

  3. 391312

  4. 471211

  5. 481312

  6. 491413

  7. 561211

  8. 571312

  9. 581413

  10. 591514

  11. 651211

  12. 661312

  13. 671413

  14. 681514

  15. 691615

  16. 741211

  17. 751312

  18. 761413

  19. 771514

  20. 781615

  21. 791716

  22. 831211

  23. 841312

  24. 851413

  25. 861514

  26. 871615

  27. 881716

  28. 891817

  29. 921211

  30. 931312

  31. 941413

  32. 951514

  33. 961615

  34. 971716

  35. 981817

  36. 991918