Digit sum

How many are three-digit numbers that have a digit sum of 6?


n =  21


The equations have the following integer solutions:
6 = a+b+c

Number of solutions found: 210
a1=1, b1=-7, c1=12
a2=1, b2=-6, c2=11
a3=1, b3=-5, c3=10
a4=1, b4=-4, c4=9
a5=1, b5=-3, c5=8
a6=1, b6=-2, c6=7
a7=1, b7=-1, c7=6
a8=1, b8=0, c8=5
a9=1, b9=1, c9=4
a10=1, b10=2, c10=3
a11=1, b11=3, c11=2
a12=1, b12=4, c12=1
a13=1, b13=5, c13=0
a14=1, b14=6, c14=-1
a15=1, b15=7, c15=-2
a16=1, b16=8, c16=-3
a17=1, b17=9, c17=-4
a18=1, b18=10, c18=-5
a19=1, b19=11, c19=-6
a20=1, b20=12, c20=-7
a21=2, b21=-7, c21=11
a22=2, b22=-6, c22=10
a23=2, b23=-5, c23=9
a24=2, b24=-4, c24=8
a25=2, b25=-3, c25=7
a26=2, b26=-2, c26=6
a27=2, b27=-1, c27=5
a28=2, b28=0, c28=4
a29=2, b29=1, c29=3
a30=2, b30=2, c30=2
a31=2, b31=3, c31=1
a32=2, b32=4, c32=0
a33=2, b33=5, c33=-1
a34=2, b34=6, c34=-2
a35=2, b35=7, c35=-3
a36=2, b36=8, c36=-4
a37=2, b37=9, c37=-5
a38=2, b38=10, c38=-6
a39=2, b39=11, c39=-7
a40=3, b40=-7, c40=10
a41=3, b41=-6, c41=9
a42=3, b42=-5, c42=8
a43=3, b43=-4, c43=7
a44=3, b44=-3, c44=6
a45=3, b45=-2, c45=5
a46=3, b46=-1, c46=4
a47=3, b47=0, c47=3
a48=3, b48=1, c48=2
a49=3, b49=2, c49=1
a50=3, b50=3, c50=0
a51=3, b51=4, c51=-1
a52=3, b52=5, c52=-2
a53=3, b53=6, c53=-3
a54=3, b54=7, c54=-4
a55=3, b55=8, c55=-5
a56=3, b56=9, c56=-6
a57=3, b57=10, c57=-7
a58=4, b58=-7, c58=9
a59=4, b59=-6, c59=8
a60=4, b60=-5, c60=7
a61=4, b61=-4, c61=6
a62=4, b62=-3, c62=5
a63=4, b63=-2, c63=4
a64=4, b64=-1, c64=3
a65=4, b65=0, c65=2
a66=4, b66=1, c66=1
a67=4, b67=2, c67=0
a68=4, b68=3, c68=-1
a69=4, b69=4, c69=-2
a70=4, b70=5, c70=-3
a71=4, b71=6, c71=-4
a72=4, b72=7, c72=-5
a73=4, b73=8, c73=-6
a74=4, b74=9, c74=-7
a75=5, b75=-7, c75=8
a76=5, b76=-6, c76=7
a77=5, b77=-5, c77=6
a78=5, b78=-4, c78=5
a79=5, b79=-3, c79=4
a80=5, b80=-2, c80=3
a81=5, b81=-1, c81=2
a82=5, b82=0, c82=1
a83=5, b83=1, c83=0
a84=5, b84=2, c84=-1
a85=5, b85=3, c85=-2
a86=5, b86=4, c86=-3
a87=5, b87=5, c87=-4
a88=5, b88=6, c88=-5
a89=5, b89=7, c89=-6
a90=5, b90=8, c90=-7
a91=6, b91=-7, c91=7
a92=6, b92=-6, c92=6
a93=6, b93=-5, c93=5
a94=6, b94=-4, c94=4
a95=6, b95=-3, c95=3
a96=6, b96=-2, c96=2
a97=6, b97=-1, c97=1
a98=6, b98=0, c98=0
a99=6, b99=1, c99=-1
a100=6, b100=2, c100=-2
a101=6, b101=3, c101=-3
a102=6, b102=4, c102=-4
a103=6, b103=5, c103=-5
a104=6, b104=6, c104=-6
a105=6, b105=7, c105=-7
a106=7, b106=-7, c106=6
a107=7, b107=-6, c107=5
a108=7, b108=-5, c108=4
a109=7, b109=-4, c109=3
a110=7, b110=-3, c110=2
a111=7, b111=-2, c111=1
a112=7, b112=-1, c112=0
a113=7, b113=0, c113=-1
a114=7, b114=1, c114=-2
a115=7, b115=2, c115=-3
a116=7, b116=3, c116=-4
a117=7, b117=4, c117=-5
a118=7, b118=5, c118=-6
a119=7, b119=6, c119=-7
a120=8, b120=-7, c120=5
a121=8, b121=-6, c121=4
a122=8, b122=-5, c122=3
a123=8, b123=-4, c123=2
a124=8, b124=-3, c124=1
a125=8, b125=-2, c125=0
a126=8, b126=-1, c126=-1
a127=8, b127=0, c127=-2
a128=8, b128=1, c128=-3
a129=8, b129=2, c129=-4
a130=8, b130=3, c130=-5
a131=8, b131=4, c131=-6
a132=8, b132=5, c132=-7
a133=9, b133=-7, c133=4
a134=9, b134=-6, c134=3
a135=9, b135=-5, c135=2
a136=9, b136=-4, c136=1
a137=9, b137=-3, c137=0
a138=9, b138=-2, c138=-1
a139=9, b139=-1, c139=-2
a140=9, b140=0, c140=-3
a141=9, b141=1, c141=-4
a142=9, b142=2, c142=-5
a143=9, b143=3, c143=-6
a144=9, b144=4, c144=-7
a145=10, b145=-7, c145=3
a146=10, b146=-6, c146=2
a147=10, b147=-5, c147=1
a148=10, b148=-4, c148=0
a149=10, b149=-3, c149=-1
a150=10, b150=-2, c150=-2
a151=10, b151=-1, c151=-3
a152=10, b152=0, c152=-4
a153=10, b153=1, c153=-5
a154=10, b154=2, c154=-6
a155=10, b155=3, c155=-7
a156=11, b156=-7, c156=2
a157=11, b157=-6, c157=1
a158=11, b158=-5, c158=0
a159=11, b159=-4, c159=-1
a160=11, b160=-3, c160=-2
a161=11, b161=-2, c161=-3
a162=11, b162=-1, c162=-4
a163=11, b163=0, c163=-5
a164=11, b164=1, c164=-6
a165=11, b165=2, c165=-7
a166=12, b166=-7, c166=1
a167=12, b167=-6, c167=0
a168=12, b168=-5, c168=-1
a169=12, b169=-4, c169=-2
a170=12, b170=-3, c170=-3
a171=12, b171=-2, c171=-4
a172=12, b172=-1, c172=-5
a173=12, b173=0, c173=-6
a174=12, b174=1, c174=-7
a175=13, b175=-7, c175=0
a176=13, b176=-6, c176=-1
a177=13, b177=-5, c177=-2
a178=13, b178=-4, c178=-3
a179=13, b179=-3, c179=-4
a180=13, b180=-2, c180=-5
a181=13, b181=-1, c181=-6
a182=13, b182=0, c182=-7
a183=14, b183=-7, c183=-1
a184=14, b184=-6, c184=-2
a185=14, b185=-5, c185=-3
a186=14, b186=-4, c186=-4
a187=14, b187=-3, c187=-5
a188=14, b188=-2, c188=-6
a189=14, b189=-1, c189=-7
a190=15, b190=-7, c190=-2
a191=15, b191=-6, c191=-3
a192=15, b192=-5, c192=-4
a193=15, b193=-4, c193=-5
a194=15, b194=-3, c194=-6
a195=15, b195=-2, c195=-7
a196=16, b196=-7, c196=-3
a197=16, b197=-6, c197=-4
a198=16, b198=-5, c198=-5
a199=16, b199=-4, c199=-6
a200=16, b200=-3, c200=-7
a201=17, b201=-7, c201=-4
a202=17, b202=-6, c202=-5
a203=17, b203=-5, c203=-6
a204=17, b204=-4, c204=-7
a205=18, b205=-7, c205=-5
a206=18, b206=-6, c206=-6
a207=18, b207=-5, c207=-7
a208=19, b208=-7, c208=-6
a209=19, b209=-6, c209=-7
a210=20, b210=-7, c210=-7

Calculated by our Diofant problems and integer equations.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
See also our permutations calculator.
Would you like to compute count of combinations?

Next similar math problems:

  1. Divisible by 5
    175px-5th_MarDiv How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
  2. Toy cars
    numbers2_13 Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
  3. Math test
    numbers_1 In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?
  4. Tram
    tramvaj-skoda In the three-part tram went 206 passengers in front of others, 226 after others and in the middle half of all. How many passengers went in tram total?
  5. Logik game
    logik-game Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numbe
  6. Pages of book
    books_2 Lenka calculated that if every day to read 16 pages of the book, read a book a day earlier than had read only 14 pages a day. How many pages has this book?
  7. Farm2
    pecene_kure The farm bred turkeys, geese, hens and chickens. Everything is 400. Turkeys and geese a hen are 150. No hen has more than one chicken, but some hens has no chick. Half of them is also a quarter of the chickens. When the turkey subtracting 15, we get 75. Ho
  8. Glass with icecream
    zmrzlina_7 We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?
  9. Mushrooms
    mushrooms-01 For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day?
  10. Football league
    football_1 In the 2nd football league plays each of the 16 participants with each opponent twice. For every victory gets 3 points, 1 point for a draw, a defeat none. After the competition was team with 54 points and 12 defeats at 9th place. How many times have won?
  11. Children
    car_game Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them?
  12. Donuts
    buchty_1 In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip?
  13. Apples 2
    apples_2 How many apples were originally on the tree, if the first day fell one third, the second day quarter of the rest and on tree remained 45 apples?
  14. Driving school
    bmw-autoskola Driving final exam involving 10 attendants. The exam consists of three parts. 2 fails at test (quiz) and 6 students fails on car skills test on playground (slalom between the cone). The practical part of the test - driving in town in the real traffic - al
  15. Remainder
    numbers2_35 A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
  16. Magic number
    prof_einstein_1 The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
  17. Divisibility
    numbers_29 Write all the integers x divisible by seven and eight at the same time for which the following applies: 100