Here's another math puzzle. ;D

"Consider a string of n 7's, i.e., 7777...77, into which + signs are inserted to produce an arithmetic expression. For example, 7+77+777+7+7=875 could be obtained from eight 7's. For how many values of n could we insert + signs so that the resulting expression has a value of 7000?"

From the 2004 AIME II.

Question

Here's another math puzzle. ;D

"Consider a string of n 7's, i.e., 7777...77, into which + signs are inserted to produce an arithmetic expression. For example, 7+77+777+7+7=875 could be obtained from eight 7's. For how many values of n could we insert + signs so that the resulting expression has a value of 7000?"

From the 2004 AIME II.

anonymous · Answer

well...

7*10=70
7*100=700
7*1000=7000

so 1000 7's? or n = 1000? unless there is something deeper to this problem...

anonymous · Answer

Not "what values of n" but "how many values of n".

anonymous · Answer

n = 28 i.e, 777 + 777 + 777 + .... 9 times + 7 = 7000

anonymous · Answer

Oh I am sorry there are two values of n 3 and 1

anonymous · Answer

False, that is not the answer.

anonymous · Answer

n = 1000, n = 100, n=28 hence 3 values

anonymous · Answer

sorry one value is 190 not 100

anonymous · Answer

Here's the solution for those who are interested. http://www.artofproblemsolving.com/Wiki/index.php/2004_AIME_II_Problems/Problem_14

anonymous · Answer

hey will take sometime I just found out there can be many such values