February 2026
Problem of the Month

Sum Thing Special
by Sidney Kravitz in GAMES

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:

The sixteen consecutive integers from 11 through 26 add up to 296.
The thirty-seven consecutive integers from -10 through 26 add up to 296.
The five hundred ninety-two consecutive integers from -295 through 296 add up to 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

Send any comments or questions to: David Pleacher