12It is divisible by 3 and by 4.[5]4.Subtract the last digit from twice the rest.

324: it is divisible by 3 and by324: 32 2 4 = 60.

13Form the alternating sum of blocks of three from right to left.[6]2,911,272: 2 + 911 272 = 637Add 4 times the last digit to the rest. 637: 63 + 7 4 = 91, 9 + 1 4 = 13.Subtract 9 times the last digit from the rest. 637: 63 63 = 0.14It is divisible by 2 and by 7.[5]224: it is divisible by 2 and by7.Add the last two digits to twice the rest. The answer must be divisible by 14.364: 3 2 + 64 = 70.1764: 17 2 + 64 = 98.155.

It is divisible by 3 and by 5.[5]

390: it is divisible by 3 and by

16If the thousands digit is even, examine the number formed by the last three digits.254,176: 176.If the thousands digit is odd, examine the number formed by the last three digits plus 8.3,408: 408 + 8 = 416.Add the last two digits to four times the rest. 176: 1 4 + 76 = 80.1168: 11 4 + 68 = 112.Examine the last four digits.[1][2]

157,648: 7,648 = 478 16.

17

Subtract 5 times the last digit from the rest. 221: 22 1 5 = 17.

189.

It is divisible by 2 and by 9.[5]

342: it is divisible by 2 and by

19

Add twice the last digit to the rest.

437: 43 + 7 2 = 57.

20It is divisible by 10, and the tens digit is even.360: is divisible by 10, and 6 is even.If the number formed by the last two digits is divisible by 20. 480: 80 is divisible by 20.

Squaring numbers made up of threesChoose a a number made up of threes.The square is made up of:one fewer 1 than there are repeating 3'szeroone fewer 8 than there are repeating 3's(same as the 1's in the square)nine.Example:

If the number to be squared is 3333:The square of the number has:three 1's (one fewer thandigits in number)next digit is 0three 8's (same number as 1's)a final 9So 3333 3333 = 11108889.

1___

1___

1___

_0__

__8_

__8_

__8_

___9

See the pattern?If the number to be squared is 333:The square of the number has:two 1'snext digit is 0two 8'sa final 9So 333 333 = 110889.

1 1 _ _ _ _ __ _ _ 0 _ _ __ _ _ _ 8 8 __ _ _ _ _ _ 9

Squaring a 2 digit number ending in 1Take a 2 digit number ending in 1.Subtract 1 from the number.Square the difference.Add the difference twice to its square.Add 1.Example:If the number is 41, subtract 1: 41 1 = 40.40 40 = 1600 (square the difference).1600 + 40 + 40 = 1680 (add the difference twiceto its square).1680 + 1 = 1681 (add 1).So 41 41 = 1681.See the pattern?For 71 71, subtract 1: 71 1 = 70.70 70 = 4900 (square the difference).4900 + 70 + 70 = 5040 (add the difference twiceto its square).5040 + 1 = 5041 (add 1).So 71 71 = 5041.

Find the difference of the squares of twoconsecutive 2 digit numbersSelect two consecutive 2 digit numbers.Add the two 2 digit numbers!Examples:24 + 25 = 49. (Try it on a calculator and see, or if you're really sharp, do it

mentally: 24 24 = 576, 25 25 = 625, 625

576 = 49.)

If 63 and 64 are selected, then 63 + 64 = 127. (For larger number addition, do it in steps: 63 + 64 = 63 + 60 + 4 = 123 + 4 = 127.)