To make a decent sized triangle start in cell Z1. Enter a 1.
Enter a 1 in Y2 and AA2.
Enter a 1 in X3 and AB3. In Z3 enter the sum of Y2 and AA2.
Enter a 1 in W4 and AC4. In Y4 enter the sum of X3 and Z3. In AA4 enter the sum of Z3 and AB3.
Enter a 1 in V5 and AD5. In X5 enter the sum of V4 and Y4. In Z5 enter the sum of Y4 and AA4. In AB5 enter the sum of AA4 and AC4.
You should start to see a pattern. Enter some more rows using the pattern.
Can you see the powers of 11? 11^0=? 11^1=? 11^2=? 11^3=? 11^6=?
Can you find a run of triangle numbers? (Formed by adding numbers 1, 2, 3, 4...)
If you add two adjacent numbers in the line of triangle numbers what type of number do you get?
Find the sum of the numbers in each row? What pattern is this?
Find a row whose second number is a prime number. What do you notice about the other numbers in the same row and in one of the diagonals that leads from it?
If there are 10 donuts on a menu and you want 2 what are the possible combinations? What if you want 3 donuts, or 4, how many combinations are there? Note that Pascal's triangle tells you the number of combinations where there is no repetition of items chosen so you have to choose 2, 3 or 4 distinct donuts, not 2 or 3 of the same kind. Allowing repeated choices changes the calculations. Just imagine that there is only one of each type of donut left!
If you have 5 cards with a single letter on each one, A, B, C, D, E, how many different letters can you obtain if you pull out one card? (That was easy!) How many different combinations of cards can you obtain if you pull out 2 cards? (AB, AC, etc). How many combinations of cards can you obtain if you pull out 3 cards? (ABC, ABD, ABE, etc. Note that BAC is equivalent to ABC). How many combinations of cards can you obtain if you pull out 4 cards? (ABCD, etc.) How many combinations of cards can you obtain if you pull out 5 cards? You can either work out the answers by writing down the combinations or you can solve the problem by using the triangle.
Going back to the ice cream vans problem, how many positions are there for 1 van on a grid of 26 street nodes? How many combinations of position are there for 2 vans on a grid of 26 street nodes? How many combinations of position are there for 3 vans on a grid of 26 street nodes? How many combinations of position are there for 3 vans on a grid of 26 street nodes? For 6 vans? (The original problem.)
If there is a national lottery that requires contestants to choose 6 numbers from 49, how many combinations of numbers are there?
For a full pack of cards (52) how many different combinations of cards can you get if you deal 1? How many combinations if you deal 2 cards? 4 cards? 13 cards? (If your triangle doesn't go this far then open the completed one from the K drive).