Number Play

Any natural number can be written

Any natural number can be written as a sum of consecutive numbers in various ways. For example: 15 = 7+8 = 4+5+6 = 1+2+3+4+5. Odd numbers can always b

Even ± even = even

Even ± even = even, odd ± odd = even, odd ± even = odd. When placing + and - signs between 4 consecutive numbers, all 8 possible expressions have the

A number is divisible by 10

A number is divisible by 10 if its units digit is 0, by 5 if units digit is 0 or 5, and by 2 if units digit is even. This works because all place valu

A number is divisible by 9

A number is divisible by 9 if the sum of its digits is divisible by 9, and by 3 if the sum of digits is divisible by 3. This works because 10 ≡ 1 (mod

A number is divisible by 11

A number is divisible by 11 if the alternating sum of its digits (starting from units place) is divisible by 11. This works because place values alter