Circle 2 Problem 6 Palindrome Worksheet With Answers - 2011-2012
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5Number Sense
2011/2012 Circle 2 Problem 6
Problem
The Palindromic Two-Step (suitable for groups of four students)
A palindrome is an expression which is the same written forwards as backwards. For example, 2,
44, 101, 8118, ‘race car’ and ‘radar’ are palindromes, while 13, 24, 245, and ‘auto’ are not.
K Y A
A
K
The number 13 is not a palindrome, but if you re-
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verse its digits and then sum the two numbers, you
get 13 + 31 = 44, which is a palindrome. Numbers
like this are called one-step palindromes.
34566543
The number 37 is also not a palindrome, but if you reverse its digits and
37
68
add, you get 37 + 73 = 110, not a palindrome. But if you repeat this
73
86
process, reversing the digits of 110 and adding, you get 110 + 011 = 121
110
154
which is a palindrome. Numbers like this are called two-step palindromes.
011
451
The number 68 is a three-step palindrome:
121
605
506
1111
a) Working in groups of four, test all the numbers from 10 to 70 and discover how many additonal
steps are required to achieve a palindrome.
Have one group member do the numbers 10
25, one do 26
40, one do 41
55, and one do
56
70.
As you work, fill in the chart below, identifying each number as a one-step, two-step, three-step,
or four-step palindrome, and state the palindromic sum.
Number of
Zero-Step
One-Step
Two-Step
Three-Step Four-Step
Steps
1, 2, 3, 4, 5, 6, 7,
13,
37,
68,
8, 9, 11, 22, 33,
44, 55, 66, 77,
88, 99
Number
1, 2, 3, 4, 5, 6, 7,
44,
121,
1111,
8, 9, 11, 22, 33,
44, 55, 66, 77,
Final
88, 99
Palindrome
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