2. It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.

3. 1 First we start off with a triangle of ones 11 11 11 11 Then we add the left and right number together on the second row 2 Continue with this addition for each line 33 446

4. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 1151054551365300350056435 47852343705235105151 1 16 120 560 1820 4368 8008 11440 12870 11220 7128 3048 940 340 120 16 1 1171366802380618812376194482431024090183481017639881280460136171 1 18 153 816 3060 8568 18564 31824 43758 48400 42438 28524 14164 5268 1740 596 153 18 1 119171969387611628271325038875582921589083870962426881943270082336749171191 1 20 190 1140 4845 15504 38760 77520 125970 167740 182996 161800 113650 62120 26440 9344 3085 920 190 20 1 Just imagine 40 rows of a Triangle!

5. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 Each row has a reference number The very top is Row 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 The sum of all the numbers in a row = 2 Row Number The sum of row 6 = 2 6 or 64 What is the sum of the eighth row? The answer is 2 8 or 256

6. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 Each number or element in a row has a reference number starting with the number 1. The first element is always element zero All of these 1’s are element 0 The next number in each row would be element 1 Let’s look at the 6 th row! 1615201561 Element 0 Element 1 Element 2 Element 3 Element 4 Element 5 Element 6

7. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 Let’s find the 3 rd element in 6 th row We’re at the 6 th rowNow let’s go to the 3 rd element 01 2 3

8. _______ 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 Here is the 3 rd element in 6 th row 1 2 3 Find 6 C 3 (nCr) or the 6 th row choose 3 rd element r!(n-r)! n! _______ 3×2×1(6-3)! 6×5×4×3×2×1 _____ 6(3)! 720 _____ 6(3×2×1) 720 _____ 36 720 = 20 “!” is a factorial. Start with the number and multiply by every sequential number down to 1 5! = 5×4×3×2×1 or 120 10! = 10×9×8×7×6×5×4×3×2×1 or 3,628,800

9. 15! 5!(15-5)! _______ Let’s find the 5 element in the 15 th row We are finding nCr or 15 C 5. We are using our formula with n being the row and r being the element. 5 C 15 = nCr = r!(n-r)! n! _______ 1307674368000 120(3628800) _______

10. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1 Add together the two number above the 5 th spot. Go to the 15 th rowNow over to where the 5 th element would be 3003

11. 1 11 1 2 1 1331 1 4 6 4 1 1510 51 1 6 15 20 15 6 1 172135 2171 1 8 28 56 70 56 28 8 1 193684126 843691 1 10 45 120 210 252 210 120 45 10 1 11155165330462 33016555111 1 12 66 220 495 792 924 792 495 0 66 12 1 1137828671512871716 12874956678131 1 14 91 364 1001 2002 3003 3432 3003 1782 561 144 91 14 1