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How many positive three-digit integers less than 500 have at least two digits that are the same?

 Mar 18, 2022
 #1
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100  101  110  111  112  113  114  115  116  117  118  119  121  122  131  133  141  144  151  155  161  166  171  177  181  188  191  199  200  202  211  212  220  221  222  223  224  225  226  227  228  229  232  233  242  244  252  255  262  266  272  277  282  288  292  299  300  303  311  313  322  323  330  331  332  333  334  335  336  337  338  339  343  344  353  355  363  366  373  377  383  388  393  399  400  404  411  414  422  424  433  434  440  441  442  443  444  445  446  447  448  449  454  455  464  466  474  477  484  488  494  499  Total =  112 such 3-digit integers.

 Mar 18, 2022
 #2
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Nice work guest, let's see if I get the same answer  laugh

 

How many positive three-digit integers less than 500 have at least two digits that are the same?

 

how many have the units and tens digit the same?   10*4 = 40

How many have the units and hudreds the same?     4*10=40

How many have the tens and hudreds the same?     4*10=40

How many have all 3 the same?    4 (must subtract twice becasue it has already been counted 3 times)

so how many have at least 2 the same = 120-8 = 112

 

laughcoollaugh

 Mar 19, 2022
edited by Melody  Mar 19, 2022

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