Difference between revisions of "2016 AMC 10B Problems/Problem 24"

(Solution)
(Solution)
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==Solution==
 
==Solution==
 
Answer is (D) for those of you wondering (verified by coding). Still need solution.
 
Answer is (D) for those of you wondering (verified by coding). Still need solution.
 +
abcd that satisfy problem conditions:
 +
1234 1357 1482 2345 2468 2470 2593 3456 3579 3581 4567 4692 5678 5680 6789 6791 8890
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2016|ab=B|num-b=23|num-a=25}}
 
{{AMC10 box|year=2016|ab=B|num-b=23|num-a=25}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 15:48, 21 February 2016

Problem

How many four-digit integers $abcd$, with $a \not\equiv 0$, have the property that the three two-digit integers $ab<bc<cd$ form an increasing arithmetic sequence? One such number is $4692$, where $a=4$, $b=6$, $c=9$, and $d=2$.

$\textbf{(A)}\ 9\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 17\qquad\textbf{(E)}\ 20$


Solution

Answer is (D) for those of you wondering (verified by coding). Still need solution. abcd that satisfy problem conditions: 1234 1357 1482 2345 2468 2470 2593 3456 3579 3581 4567 4692 5678 5680 6789 6791 8890

See Also

2016 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
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 AMC 10 Problems and Solutions

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