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With the first one of square number surprises we found 1 + 4 is 5 - 1 = 4, 4+9=13-1=12 which is also in the 4x table and 9+16=25-1=24 which is again also in the 4x table so if you add any two consecutive square numbers and subtract 1 the answer will be in the 4x table. In the second one, 3x3=9-1=8, 5x5=25-1=24, 7x7=49-1=48 and 9x9=81-1=80 so if you square any odd number and subtract 1 the answer will be in the 8x table. In the third one, 1x3=3+1=4 which is a square number, 3x5=15+1=16 which is also a square number and 5x7=35+1=36 which again is a square number so if you multiply two consecutive odd numbers and add 1 you will get an even square number. Finally, the fourth one, 2x4=8+1=9, 4x6=24+1=25 and 6x8=48+1=49 the answers are all odd square numbers so if you times two consecutive even numbers and add 1 you will get an odd square number. Thank you for reading! By Emily & Luke.