Though not obvious, there is a definite pattern in the following table of numbers. Please fill in the last column.
Solution by Peter Denton, East Grand Rapids High School
There are three separate diagonal sequences. The first one is the Fibonacci
sequence. It starts with the 1 in the first column, then goes to the 1 at the
bottom of the next column and proceeds diagonally. This creates the sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55; therefore, the
bottom number in the last column must be 89. The
second sequence, starting with 2 in the first column, is a sequence of primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29; therefore,
the top number in the last column mustbe 31.The
third sequence, starting with 3 in the first column, is a sequence of odd numbers:
3, 5, 7, 9, 11, 13, 15, 17, 19, 21; therefore,
the middle number in the last column must be 23.
Also solved by: Alex Bordyukov, Eva Dou (Grosse Pointe South H.S.), Kevin Soubly (Detroit Catholic Central H.S.), Patrick Julius, Milena Soc (Ann Arbor Huron H.S.), Keith DeBoer (Forest Hills Eastern H.S.), Adam Carlson (Forest Hills Northern H.S.), Young-Key Chung (Troy Athens H.S.), Sunil Abraham (Adrian H.S.), Fares Alghanem (Grand Blanc M.S.), Mark Bourne (Midland Dow H.S.), John Hayes (East Grand Rapids H.S.), Candice Penn, Katelyn Watts (Ladywood H.S), Jonathan Bomar (Big Rapids H.S.), Teresa Wang (Plymouth-Canton Ed. Park), Ramsey Gilbertsen (Marquette H.S.), Zita Anderson (Charlevoix H.S.), Pascal Carole, Remy Carole (Saginaw Arts and Sciences Academy).