Special Numbers Stage 4 Year 7 Press CtrlA

Palindromic Numbers Palindromes are numbers or words that are the same backwards as forwards. Examples madam 1221 Mum 100001 Dad 12. 21 1991 Hannah 11/1/11 toot 42 2

Palindromic Words What about? STEP NOT ON PETS MADAM I’M ADAM LEPERS REPEL NO LEMONS, NO MELON DENNIS AND EDNA SINNED ROTATOR REVIVER ABLE WAS I ERE I SAW ELBA A MAN, A PLAN, A CANAL, PANAMA SUMS ARE NOT SET AS A TEST ON ERASMUS 42 3

Palindromic Numbers What about Number Sentences? 11 112 1113 11114 111115 1111116 11111117 11118 = = = = 1 12321 123454321 1234567654321 123456787654321 42 4

Palindromic Numbers More Number Sentences? 110 = 1 111 = 11 112 = 121 113 = 1331 114 = 14641 42 5

Palindromic Numbers More Number Sentences? A palindromic number can be generated from any number. All you do is to continually add a number to its reversal until you get a palindrome. 123 + 321 = 444 86 154 605 1210 + + 68 = 451 = 506 = 0121 = 154 605 1210 1331 Now try one yourself!!! 42 6

Square Numbers Can be made into squares. 1 4 9 16 1 x 1 3 x 3 12 2 x 2 32 4 x 4 42 22 25 5 x 5 52 36 6 x 6 62 42 7

Triangular Numbers Can be made into triangles. 1 1 3 6 10 15 21 1+2+3+4+5 1+2+3+4+5+6 42 8

Sum of Triangular Numbers What type of number is the sum of consecutive triangular numbers? Square Numbers 1+3 3+6 6+10 10+15 15+21 4 9 16 25 36 22 42 32 52 62 42 9