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The-number-of-times-the-digit-3-will-be-written-when-listing-the-integers-from-1-to-1000-is-




Question Number 48543 by Pk1167156@gmail.com last updated on 25/Nov/18
The number of times the digit 3 will  be written when listing the integers  from 1 to 1000 is
Thenumberoftimesthedigit3willbewrittenwhenlistingtheintegersfrom1to1000is
Answered by mr W last updated on 25/Nov/18
one−digit−numbers:  3⇒1 number⇒1 time    two−digit−numbers:  x3⇒ 8 numbers⇒8 times  3x⇒ 9 numbers⇒9 times  33⇒ 1 number⇒2 times    three−digit−numbers:  xy3 ⇒8×9=72 numbers⇒72 times  x3y ⇒8×9=72 numbers⇒72 times  3xy ⇒9×9=81 numbers⇒81 times  x33 ⇒8 numbers⇒16 times  33x ⇒9 numbers⇒18 times  3x3 ⇒9 numbers⇒18 times  333 ⇒1 numbers⇒3 times    Σtimes=1+8+9+2+72+72+81+16+18+18+3  Σtimes=300
onedigitnumbers:31number1timetwodigitnumbers:x38numbers8times3x9numbers9times331number2timesthreedigitnumbers:xy38×9=72numbers72timesx3y8×9=72numbers72times3xy9×9=81numbers81timesx338numbers16times33x9numbers18times3x39numbers18times3331numbers3timesΣtimes=1+8+9+2+72+72+81+16+18+18+3Σtimes=300
Answered by mr W last updated on 27/Nov/18
3xy: 10×10=100 times    x3y: 9×10=90 times  3y: 10 times    xy3: 9×10=90 times  x3: 9 times  3: 1 time    Σtimes=100+100+100=300
3xy:10×10=100timesx3y:9×10=90times3y:10timesxy3:9×10=90timesx3:9times3:1timeΣtimes=100+100+100=300

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