SOLUTION: how many even four digit numbers less than 8999 can be formed if the sum of the middle two numbers is 13.

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Question 1152611: how many even four digit numbers less than 8999 can be formed if the sum of the middle two numbers is 13.
Answer by ikleyn(52781) About Me  (Show Source):
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how many even four digit numbers less than 8999 can be formed if the sum of the middle two highlight%28cross%28numbers%29%29 digits is 13. 


Since the sum of the middle two digits is 13, these two digits in the middle are these 6 pairs

    49  58  67  76  85  94

and there is NO other possibilities.



Next, the last digit (the "ones" digit) is any of five even numbers 0, 2, 4, 6, 8,

while the leftmost digit can be any of eight numbers 1,2,3,4,5,6,7,8.



Therefore, the answer to the problem's question is the product

           6*5*8 = 240.