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Of the three-digit integers greater than $500$, how many have two digits that are equal to each other and the remaining digit different from the other two

 
 Nov 20, 2021
 #1
avatar+391 
+1

Hello Guest,

 

Of the three-digit integers greater than $500$, how many have two digits that are equal to each other and the remaining digit different from the other two

 

500, 511, 522, 533, 544, 566, 577, 588, 599 (10)

600, 611, 622, 633, 644, 655, 677, 688, 699 (10)

700, 711, 722, 733 ,744 ,755 ,766, 788, 799 (10)

800, 811, 822, 833, 844, 855, 866, 877, 899 (10)

900, 911, 922, 933, 944, 955, 966, 977, 988 (10)

505, 515, 525, 535, 545, 565, 575, 585, 595 (10)

606, 616, 626, 636, 646, 656, 676, 686, 696 (10)

707, 717, 727, 737, 747, 757, 767, 787, 797 (10)

808, 818, 828, 838, 848, 858, 868, 878, 898 (10)

909, 919, 929, 939, 949, 959, 969, 979, 989 (10)

550, 551, 552, 553, 554, 556, 557, 558, 559 (10)

660, 661, 662, 663, 664, 665, 667, 668, 669 (10)

770, 771, 772, 773, 774, 775, 776, 778, 779 (19)

880, 881, 882, 883, 884, 885, 886, 887, 889 (10)

 

This gives 140 numbers, if it were so desired.

 

Hope that was helpful. ^^

 

Straight

 
 Nov 20, 2021
 #3
avatar+391 
+1

I forgot-

 

990, 991, 992, 993, 994, 995, 996, 997, 998 (9) So there are actually 149 integers.

 

Also, it is not (19) I meant (10). Umm, can someone explain which answer is right and why?

 

Straight

 
Straight  Nov 20, 2021
 #4
avatar
+1

Your rows and columns are: 9  x  14  ==126

And you are missing one row of "9s" ==990, 991, 992, 993, 994, 995, 996, 997, 998 ==9

126 + 9 ==135 - such integers.

 
Guest Nov 20, 2021
 #5
avatar+391 
0

Okay, I am actually sorry,

 

I must concentrate on myself. sad

 

Straight

 
Straight  Nov 20, 2021
 #2
avatar
+1

There are:

 

(500, 505, 511, 515, 522, 525, 533, 535, 544, 545, 550, 551, 552, 553, 554, 556, 557, 558, 559, 565, 566, 575, 577, 585, 588, 595, 599, 600, 606, 611, 616, 622, 626, 633, 636, 644, 646, 655, 656, 660, 661, 662, 663, 664, 665, 667, 668, 669, 676, 677, 686, 688, 696, 699, 700, 707, 711, 717, 722, 727, 733, 737, 744, 747, 755, 757, 766, 767, 770, 771, 772, 773, 774, 775, 776, 778, 779, 787, 788, 797, 799, 800, 808, 811, 818, 822, 828, 833, 838, 844, 848, 855, 858, 866, 868, 877, 878, 880, 881, 882, 883, 884, 885, 886, 887, 889, 898, 899, 900, 909, 911, 919, 922, 929, 933, 939, 944, 949, 955, 959, 966, 969, 977, 979, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998)==135 such integers.

 
 Nov 20, 2021
 #6
avatar
0

500 should NOT be included....Q asks for numbers GREATER than 500 .....

 
Guest Nov 20, 2021
 #7
avatar+115358 
+1

Of the three-digit integers greater than $500$, how many have two digits that are equal to each other and the remaining digit different from the other two

 

2 zeros :  4

1 zero : 5*2=10

the rest have no zeros

2 of 1,2,3,4      :    4*5 = 20

2 of 5,6,7,8,9   and one 1,2,3 or 4  :  5*4*2=40

2 of 5,6,7,8,9   and one 5,6,7,8,9  :  5*4*3=60

 

 

4+10+20+40+60 = 134

 
 Nov 21, 2021
edited by Melody  Nov 21, 2021

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