A certain three-digit number is the product of two different
prime numbers that end with the same digit.
The three digit number's middle digit is larger than its first
digit and smaller than its third digit.
(In other words, the tens digit is larger than its hundreds digit
and smaller than its ones digit).
What is the three-digit number?
Solution to the Problem:
There are nine answers:129 = 3 * 43
159 = 3 * 53
249 = 3 * 83
259 = 7 * 37
469 = 7 * 67
489 = 3 * 163
679 = 7 * 97
689 = 13 * 53
789 = 3 * 263
Marco Morelli sent in this analysis: First of all, all prime numbers (except 2 and 5) end with 1 or 3 or 7 or 9; however, the last digit of the two prime numbers cannot be 1 nor 9, otherwise their product would have 1 as the units digit, and a three-digit number having its hundreds digit smaller than its tens digit smaller than 1 cannot exist; so we are left with 3 or 7; now we must assume that the two prime numbers have at least 2 digits, so we end up with evaluating the following couples: 13*23 = 299 13*43 = 559 13*53 = 689 13*73 = 949 17*37 = 629 17*47 = 799 which are the only couples having a three-digit number as their product; the desired number is therefore 689. Notice that if we drop that assumption, there are other couples, such as: 3*43 = 129 3*53 = 159 3*163 = 489 3*193 = 579 3*263 = 789 7*37 = 259 7*67 = 469 7*97 = 679
Correctly solved by:
| 1. James Alarie (sent in all 9 solutions) | Flint, Michigan |
| 2. Chris White |
St. Marks Elementary, Colwich, Kansas |
| 3. Celton Perry (sent in 2 solutions) |
Mountain View High School, Mountain View, Wyoming |
| 4. SreeRoopa Sankararaman | Singapore, Singapore |
| 5. Marco Morelli (sent in all 9 solutions) | Fermo, Italy |
| 6. Chris Striniger |
Mountain View High School, Mountain View, Wyoming |
| 7. Keagan Genzer |
Mountain View High School, Mountain View, Wyoming |
| 8. Breanna Hood |
Mountain View High School, Mountain View, Wyoming |
| 9. Charity Harmon |
Mountain View High School, Mountain View, Wyoming |
| 9. Kalen Rhodes |
St. Joseph High School, Westchester, Illinois |
| 10. Chelsey M. |
John F Kennedy High School, Taylor, Michigan |
| 11. Tristan Hamblin |
Mountain View High School, Mountain View, Wyoming |
| 12. Alyx Wells |
Mountain View High School, Mountain View, Wyoming |
| 13. Jessica Hamblin |
Mountain View High School, Mountain View, Wyoming |
| 14. Trenton Harmon |
Mountain View High School, Mountain View, Wyoming |
| 15. Jessica Hamblin |
Mountain View High School, Mountain View, Wyoming |
| 16. Mckinzee Walker |
Mountain View High School, Mountain View, Wyoming |
| 17. Samantha Brailsford |
Mountain View High School, Mountain View, Wyoming |
| 18. Alexis Stoddard |
Mountain View High School, Mountain View, Wyoming |
| 19. Hannah Stoddard |
Mountain View High School, Mountain View, Wyoming |
| 20. Cheyenne Dunn |
Mountain View High School, Mountain View, Wyoming |
| 21. Gage Barney |
Mountain View High School, Mountain View, Wyoming |
| 22. Dusty Q. Iorg |
Mountain View High School, Mountain View, Wyoming |
| 23. Nasima Madbouhi |
Mountain View High School, Mountain View, Wyoming |
| 24. Kayle Rippetoe |
Mountain View High School, Mountain View, Wyoming |
| 25. Mashayla Hurdsman |
Mountain View High School, Mountain View, Wyoming |
| 26. Kaylee Gross |
Mountain View High School, Mountain View, Wyoming |
| 27. Taylor Meeks |
Mountain View High School, Mountain View, Wyoming |