What is 4-H

In 4-H, H stands for Homogeneous (equal everywhere). 4 stands for Sum of nearby four terms. So in a table, if some of nearby four terms is equal everywhere then we call the arrangement as 4-H or 4H and the sum s.

In this figure

a=1;b=4;c=3;d=6;e=2;f=5;g=8;h=7;i=3

a + b + d + e = 1 + 4 + 6 + 2 = 13

b + c + e + f = 4 + 3 + 2 + 5 = 14

d + e + g + h = 6 + 2 + 8 + 7 = 23

e + f + h + i = 2 + 5 + 7 + 3 = 17

We see all these sums are different for 4-H they should all be equal, so this is NOT a 4H arrangement

However, the following arrangement

We have four groups of nearby four terms each (depicted with different colours)

a = 1; b = 9; c = 2;

d = 8; e = 3;f = 7;

g = 4; h = 6; i = 5

a + b + d + e = 1 + 9 + 8 + 3 = 21

b + c + e + f = 9 + 2 + 3 + 7 = 21

d + e + g + h = 8 + 3 + 4 + 6 = 21

e + f + h + i = 3 + 7 + 6 + 5 = 21

Hence above matrix is 4H table with sum s = 21.

With this we have opened a new treasure (millions and trillions) of 4H problems. There can be 4H problems in different structures (all types of tables etc.).

Let’s explore them now..