Problem of the Month - October 2024

A string of consecutive whole numbers that adds to 2024 is 179+180+181+182+183+184+185+186+187+188+189. 

Can you find another string of whole numbers that adds up to 2024?  

Solution

Another string of consecutive whole numbers that adds to 2024 is 77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99.  We know this because 2024= 88 x 23.  We can write 88 twenty-three times and add them to get a total of 2024.  Now starting at the middle 88, the 12^th one, move to the right and add 1, and move to the left and subtract 1.  Then again starting at the 12^th number, move two spots to the right and add 2, and move two spots to the left and subtract 2.  Keep doing this process until you get the list above.  

Can you find a string of 15 consecutive numbers whose sum is 360?