Determine a set of consecutive integers (we won't tell you how many) that add up to 296.
There are at least three solutions.
Solution to the Problem:
Here are some solutions:(1) The sixteen consecutive integers from 11 through 26 add up to 296.
(2) The thirty-seven consecutive integers from -10 through 26 add up to 296.
(3) The five hundred ninety-two consecutive integers from -295 through 296 add up to 296.
(4) The set {296}
Kamal Lohia had a nice explanation:
Solution: 296 = 2³ × 37
= 592 terms × average of ½ = -295-294-293-...0+1+2+...+294+295+296
= 16 terms × average of 18½ = 11+12+..+18+19+..+25+26
= 37 terms × average of 8 = -10-9-....+8+....+25+26
Click here to see Hari Kishan's excellent mathematical approach
One of Mr. Fortson's students sent in the set {296} with the reasoning that technically it is a set containing integers and none of them are non-consecutive. I liked the double negative here.
Correctly solved by:
| 1. Colin (Yowie) Bowey ** (found 3 solutions) | Beechworth, Victoria, Australia |
| 2. Kamal Lohia ** (found 3 solutions) | Hisar, Haryana, India |
| 3. Davit Banana ** (found 3 solutions) | Istanbul, Turkey |
| 4. Dr. Hari Kishan ** (found 3 solutions) |
D.N. College, Meerut, Uttar Pradesh, India |
| 5. Calvin Fortson |
Hinsdale School District Hinsdale, New Hampshire, USA |
| 6. One of Mr. Fortson's students |
Hinsdale School District Hinsdale, New Hampshire, USA |
| 7. Ivy Joseph ** (found 3 solutions) | Pune, Maharashtra, India |
| 8. Kelly Stubblefield ** (found 3 solutions) | Mobile, Alabama, USA |
| 9. Jocelyn Ramirez |
Central High School, Grand Junction, Colorado, USA |
| 10. Eva Hull |
Central High School, Grand Junction, Colorado, USA |
** Extra Credit