How many 4-digit numbers are there, the sum of whose digits is 11?

Question

How many 4-digit numbers are there, the sum of whose digits is 11?

Answer 1

There are 279 of them...

Surely there is a systematic way to list them. Instead however, I wrote a computer program to

do it for us. Here is the source code in C++ and the output thereof...

/******************************************/

using namespace std;

#include <iostream>

#include <stdio.h>

Go()

{

char numStrBuff[5];

for (int iLoop=1000; iLoop<=9999; iLoop++)

{

sprintf(numStrBuff,"%d",iLoop);

int thousandsDigit = (int)(numStrBuff[0]-48);

int hundredsDigit = (int)(numStrBuff[1]-48);

int tensDigit = (int)(numStrBuff[2]-48);

int unitsDigit = (int)(numStrBuff[3]-48);

if (thousandsDigit+hundredsDigit+tensDigit+unitsDigit==11)

{

cout << iLoop << " ";

}

}

}

int main()

{

Go();

}

1019 1028 1037 1046 1055 1064 1073 1082 1091 1109 1118 1127 1136 1145 1154 1163 1172 1181 1190

1208 1217 1226 1235 1244 1253 1262 1271 1280 1307 1316 1325 1334 1343 1352 1361 1370 1406 1415

1424 1433 1442 1451 1460 1505 1514 1523 1532 1541 1550 1604 1613 1622 1631 1640 1703 1712 1721

1730 1802 1811 1820 1901 1910 2009 2018 2027 2036 2045 2054 2063 2072 2081 2090 2108 2117 2126

2135 2144 2153 2162 2171 2180 2207 2216 2225 2234 2243 2252 2261 2270 2306 2315 2324 2333 2342

2351 2360 2405 2414 2423 2432 2441 2450 2504 2513 2522 2531 2540 2603 2612 2621 2630 2702 2711

2720 2801 2810 2900 3008 3017 3026 3035 3044 3053 3062 3071 3080 3107 3116 3125 3134 3143 3152

3161 3170 3206 3215 3224 3233 3242 3251 3260 3305 3314 3323 3332 3341 3350 3404 3413 3422 3431

3440 3503 3512 3521 3530 3602 3611 3620 3701 3710 3800 4007 4016 4025 4034 4043 4052 4061 4070

4106 4115 4124 4133 4142 4151 4160 4205 4214 4223 4232 4241 4250 4304 4313 4322 4331 4340 4403

4412 4421 4430 4502 4511 4520 4601 4610 4700 5006 5015 5024 5033 5042 5051 5060 5105 5114 5123

5132 5141 5150 5204 5213 5222 5231 5240 5303 5312 5321 5330 5402 5411 5420 5501 5510 5600 6005

6014 6023 6032 6041 6050 6104 6113 6122 6131 6140 6203 6212 6221 6230 6302 6311 6320 6401 6410

6500 7004 7013 7022 7031 7040 7103 7112 7121 7130 7202 7211 7220 7301 7310 7400 8003 8012 8021

8030 8102 8111 8120 8201 8210 8300 9002 9011 9020 9101 9110 9200