My daughter age 11 can't do this, and I can't help her. Could someone explain very basically how to solve it please.
Draw an X and Y plan, with the coordinates of O being your origin (0,0). Plot A with coordinates (2,0), B (3,0) and C (2,1).
Now in this question journeys are made of steps of whole-numbers length in any combination of directions left, right, up or down. Also one may retrace steps. So, for example, it is possible to travel from O to the point (2,1) by journey OAC which has length 3, it is possible to get to (2,1) by a different journey, OBAC which has length 5.
a) Starting from O, how many possible destinations (including O) are there with journeys of length
b) How many different journeys of length 3 are there starting at O and finishing at (1,0)?
c) You are given that the sum 1+2+3+....+100 = 5050
How many journeys of length 102 are there from O to coordinate (100,0)?