Digit sums of multiples of 11
1,444.2K Views
Answered
Some multiples of 11 have an even digit sum.
For example-
7*11 = 77 and 7+7 = 14, which is even;
11*11 = 121 and 1+2+1 = 4, which is even.
Do all multiples of 11 have an even digit sum?
(Prove that they do or find the smallest that does not.)
Best answer
using 11 division test we know abcdef if divisible by 11
a + c+e+(b+d+f)=2(sum of even or odd places) + some multiple of 11 having less digits then abcdef.now suppose statement in question works till n digits where n is any number then it will work for n+1 digits we just prove it works when n =2 so i did it
Your Answer
More puzzles to try-
Catch the Lying Member
A Japanese ship was en route to a mission on foreign seas. The captain of the ship felt tired and ...Read More »Toy of queen riddle
Toy of queen, Tool of thief. Always used to be unseen. Sign of Sorrow and joy. Giving all likeness borrowed. ...Read More »Lift an elephant with one hand
How can you lift an elephant with one hand?Read More »Four People on a Rickety Bridge
Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is ...Read More »How did she know?
A cheap man and his wife decide to go on a trip for their 10th anniversary. They go to Brazil ...Read More »Equation
If 1 equals 5, 2 equals 10, 3 equals 15, 4 equals 20, then what does 5 equals to?Read More »Which switch controls the bulb ??
Outside a room there are three light switches. One of switch is connected to a light bulb inside the room. ...Read More »Who am I?
You are my brother, but I am not your brother. Who am I?Read More »GALILEO’S PARADOX OF THE INFINITE
In his final written work, Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the legendary Italian polymath Galileo ...Read More »July Equals To…
If March = 43 and May = 39, what does July equals to?Read More »Crossing a Bridge riddle
Four men want to cross a bridge. They all begin on the same side. It is night and they have ...Read More »What is the parking slot number?
What is the parking spot number that the parked car occupies?Read More »Never thank me
Walk right through me, Never feel me. Always watching, Never speaking. Always lurking, Never seen. Die without me, Never thank ...Read More »Exam A+ riddle
Tom’s dad had told him that if he could get an A+ on his final exam, he could get him ...Read More »The Man in the Bar
A man walks into a bar and asks the barman for a glass of water. The barman pulls out a ...Read More »Magic Word
What word is the same if you turn it upside down and backwards?Read More »Maximum distance travelled by scooter puzzle
There is one scooter which has 2 tyres and one stepney/spare (i.e. total 3 tyres). Each Tyre can run up ...Read More »I’m teary-eyed but never cry riddle
I’m teary-eyed but never cry. Silver-tongued, but never lie. Double-winged, but never fly. Air-cooled, but never dry. What am I?Read More »Funniest Blonde
A blonde put eyeliner on her head. Why?Read More »Runs over fields riddle
It runs over fields and roads all day. Sits under the bed at night not alone, With their long tongue ...Read More »
Accenture Interview PuzzlesAdobe Interview PuzzlesAge RiddleAkbar Birbal PuzzlesAlgorithm PuzzlesAlphabet riddleAmazon Interview PuzzlesAnalytical MathematicsAptitude PuzzleBank PuzzlesBetting PuzzlesBrain TeasersCalendar PuzzlesCards PuzzlesChess Board PuzzleChess PuzzlesChristmas Puzzlecipher PuzzleCivil Services PuzzleClock time puzzleCognizant Interview PuzzlesCoins PuzzleComputational PuzzleconundrumCoronavirus PuzzleCoupondunia Interview PuzzleCritical Thinking Puzzledata analyticsData Structure Interview QuestionsDecode PuzzleDetective PuzzlesDice PuzzleDictionary Riddlesdifficult riddleEasy Math puzzlesEasy puzzlesEinstein puzzleEnglish RiddleFamily Tree Puzzlefamous puzzleFill in the blanks riddlesFinding Killer RiddlesFlipkart interview puzzlesFunny RiddlesGeneral KnowledgeGeographical PuzzleGoogle Code Jam 2014Google Interview PuzzlesGRE PuzzleHard Puzzle