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5 votes
How many binary numbers of 16 bits or less are perfect squares and have exactly five 1's in them

User Daveywc
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7.6k points

1 Answer

1 vote

Answer:

194

Step-by-step explanation:

121,361,441,484,625,729,841,961,1225,1369,1444,1521,1681,1764,1849,1936,2025,2401,2500,2601,2809,2916,3025,3249,3364,3481,3721,3844,3969,4489,4761,4900,5041,5329,5476,5625,5776,5929,6084,6241,6561,6724,6889,7056,7225,7396,7569,7744,7921,8100,8281,8649,9025,9409,9604,9801,10000,10201,10404,10609,11025,11236,11449,11664,11881,12100,12769,12996,13225,13456,13689,13924,14161,14641,14884,15129,15376,15625,15876,16129,17161,17689,17956,18225,18769,19044,19321,19600,19881,20164,20449,21025,21316,21609,21904,22201,22500,22801,23104,23409,23716,24025,24336,24649,24964,25281,25921,26244,26569,26896,27225,27556,27889,28224,28561,28900,29241,29584,29929,30276,30625,30976,31329,31684,32041,32400,32761,33124,33489,34225,34596,34969,35721,36100,36481,37249,37636,38025,38416,38809,39204,39601,40000,40401,40804,41209,41616,42025,42436,42849,43681,44100,44521,44944,45369,45796,46225,46656,47089,47524,47961,48400,48841,49729,50625,51076,51529,51984,52441,52900,53361,53824,54289,54756,55225,55696,56169,56644,57121,58081,58564,59049,59536,60025,60516,61009,61504,62001,62500,63001,63504,64009,64516,65025

I made a program in python just for this question.

How many binary numbers of 16 bits or less are perfect squares and have exactly five-example-1
User Lucca Nielsen
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8.3k points