Difference between revisions of "1988 AJHSME Problems/Problem 25"
5849206328x (talk | contribs) (New page: ==Problem== A '''palindrome''' is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three...) |
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==Problem== | ==Problem== | ||
− | A '''palindrome''' is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: <math>\boxed{1:01}</math>, <math>\boxed{4:44}</math>, and <math>\boxed{12:21}</math>. How many times during a <math>12</math>-hour period will be palindromes? | + | A '''[[palindrome]]''' is a [[whole number]] that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: <math>\boxed{1:01}</math>, <math>\boxed{4:44}</math>, and <math>\boxed{12:21}</math>. How many times during a <math>12</math>-hour period will be palindromes? |
<math>\text{(A)}\ 57 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 63 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 93</math> | <math>\text{(A)}\ 57 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 63 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 93</math> | ||
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==See Also== | ==See Also== | ||
− | + | {{AJHSME box|year=1988|num-b=24|after=Last<br>Problem}} | |
[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 22:56, 4 July 2013
Problem
A palindrome is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: , , and . How many times during a -hour period will be palindromes?
Solution
From to , the times will be of the form . There are choices for and choices for , so there are times in this period.
From to , the minutes are already determined, so there are only times in this case.
In total, there are palindromic times.
See Also
1988 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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