19: MULTIPLY CONSECUTIVE NUMBERS

SUTRA (Algorithm):

Smaller2 + Smaller

[ or ]

Larger2 - Larger

Demonstration (1): 3 x 4 = ?

3 x 4 = 32 + 3 = 9 + 3 = 12
3 x 4 = 42 - 4 = 16 - 4 = 12

Demonstration (2): 12 x 13 = ?

12 x 13 = 122 + 12 = 144 + 12 = 156
12 x 13 = 132 - 13 = 169 - 13 = 156

Demonstration (3): 25 x 26 = ?

25 x 26 = 252 + 25 = 625 + 25 = 650
25 x 26 = 262 - 26 = 676 - 26 = 650

Demonstration (4): 22 x 23 = ?

22 x 23 = 222 + 22 = 484 + 22 = 506

Demonstration (5): 201 x 202 = ?

201 x 202 = 2012 + 201 = 40401 + 201 = 40602

Demonstration (6): 209 x 210 = ?

209 x 210 = 2102 - 210 = 44100 - 210 = 43890

Verify by ACTUAL WORKING:

  1. 16 X 17 = 162 + 16 = 256 + 16 = 272
  2. 31 X 32 = 312 + 31 = 961 + 31 = 992
  3. 31 X 32 = 322 - 32 = 1024 - 32 = 992
  4. 31 X 32 = 312 + 31 = 961 + 31 = 992
  5. 32 X 33 = 322 + 32 = 1024 + 32 = 1056
  6. 39 X 40 = 402 - 40 = 1600 - 40 = 1540
  7. 22 X 24 = 4(11 x 12) = 4 x 132 = 528
  8. 33 X 36 = 9(11 x 12) = 9 x 132 = 1188