Menu Close

How-many-zeros-and-how-many-ones-are-there-in-the-numbers-from-1-to-9999-Example-in-the-number-1010-there-are-2-zeros-and-2-ones-




Question Number 53902 by mr W last updated on 27/Jan/19
How many zeros and how many ones  are there in the numbers from 1 to  9999?  Example: in the number 1010 there  are 2 zeros and 2 ones.
$${How}\:{many}\:{zeros}\:{and}\:{how}\:{many}\:{ones} \\ $$$${are}\:{there}\:{in}\:{the}\:{numbers}\:{from}\:\mathrm{1}\:{to} \\ $$$$\mathrm{9999}? \\ $$$${Example}:\:{in}\:{the}\:{number}\:\mathrm{1010}\:{there} \\ $$$${are}\:\mathrm{2}\:{zeros}\:{and}\:\mathrm{2}\:{ones}. \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 27/Jan/19
sir excellent questiin...trying to solve..  pls do not post answer till the goal is reached  ...if not succeed...then you pls upload answer
$${sir}\:{excellent}\:{questiin}…{trying}\:{to}\:{solve}.. \\ $$$${pls}\:{do}\:{not}\:{post}\:{answer}\:{till}\:{the}\:{goal}\:{is}\:{reached} \\ $$$$…{if}\:{not}\:{succeed}…{then}\:{you}\:{pls}\:{upload}\:{answer} \\ $$$$ \\ $$
Commented by Tawa1 last updated on 27/Jan/19
Good question
$$\mathrm{Good}\:\mathrm{question} \\ $$
Commented by mr W last updated on 27/Jan/19
i have not got the answer yet. please  try to solve. thanks sir!
$${i}\:{have}\:{not}\:{got}\:{the}\:{answer}\:{yet}.\:{please} \\ $$$${try}\:{to}\:{solve}.\:{thanks}\:{sir}! \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Jan/19
calculation of zdroes...  1)one digit no →use of zero→is 0→0■    2)Two digit no→when unit place →0  tength digit can be filled by any number→(1,2,3..9)  so 9 numbers →9■  3)Three digit number→unit place→0     tength place can be filled →(1,2,...9)→9ways  hundred can be filled →(1,2...8)9 ways  so total=1×9×9=81  now use of 0 in this  81 numbers=81■    Three digit no unit place→0  [also tenth place →0  hundred place →can be filled →using( 1,2,3..9)  →9 ways →9 numbdrs →e.g[100,200,..900]  use of 0 in this 9 numbers=9×2=18■    Three digit no tength place 0→unit plac(1 to9)→  hundred place →any number (1,2,3..9)  9×1×9=81  use of 0→1×81=81■    4)four dugit no  −^×   −^×  −^×  −^0 →9×9×9×1=729  −^×  −^×  −^0  −^× →9×9×1×9=729  −^×  −^0  −^×  −^× →9×1×9×9=729  −^×  −^×  −^0  −^0 →9×9×1×1=81  −^×  −^0 −^×  −^0 →9×1×9×1=81  −^×  −^0  −^0  −^× →9×1×1×9=81  use of 0 [729+729+729]×1■  use of 00[81+81+81]×2■    −^× −^0   −^0 −^0  →9×1×1×1=9  use of 000=9×3=27■  sir pls check till now to get the use of 0  we have to add ■ marked value...  pls check..  i have cslculated only use of 0 till now..
$${calculation}\:{of}\:{zdroes}… \\ $$$$\left.\mathrm{1}\right){one}\:{digit}\:{no}\:\rightarrow{use}\:{of}\:{zero}\rightarrow{is}\:\mathrm{0}\rightarrow\mathrm{0}\blacksquare \\ $$$$ \\ $$$$\left.\mathrm{2}\right){Two}\:{digit}\:{no}\rightarrow{when}\:{unit}\:{place}\:\rightarrow\mathrm{0} \\ $$$${tength}\:{digit}\:{can}\:{be}\:{filled}\:{by}\:{any}\:{number}\rightarrow\left(\mathrm{1},\mathrm{2},\mathrm{3}..\mathrm{9}\right) \\ $$$${so}\:\mathrm{9}\:{numbers}\:\rightarrow\mathrm{9}\blacksquare \\ $$$$\left.\mathrm{3}\right){Three}\:{digit}\:{number}\rightarrow{unit}\:{place}\rightarrow\mathrm{0} \\ $$$$\:\:\:{tength}\:{place}\:{can}\:{be}\:{filled}\:\rightarrow\left(\mathrm{1},\mathrm{2},…\mathrm{9}\right)\rightarrow\mathrm{9}{ways} \\ $$$${hundred}\:{can}\:{be}\:{filled}\:\rightarrow\left(\mathrm{1},\mathrm{2}…\mathrm{8}\right)\mathrm{9}\:{ways} \\ $$$${so}\:{total}=\mathrm{1}×\mathrm{9}×\mathrm{9}=\mathrm{81} \\ $$$${now}\:{use}\:{of}\:\mathrm{0}\:{in}\:{this}\:\:\mathrm{81}\:{numbers}=\mathrm{81}\blacksquare \\ $$$$ \\ $$$${Three}\:{digit}\:{no}\:{unit}\:{place}\rightarrow\mathrm{0} \\ $$$$\left[{also}\:{tenth}\:{place}\:\rightarrow\mathrm{0}\right. \\ $$$${hundred}\:{place}\:\rightarrow{can}\:{be}\:{filled}\:\rightarrow{using}\left(\:\mathrm{1},\mathrm{2},\mathrm{3}..\mathrm{9}\right) \\ $$$$\rightarrow\mathrm{9}\:{ways}\:\rightarrow\mathrm{9}\:{numbdrs}\:\rightarrow{e}.{g}\left[\mathrm{100},\mathrm{200},..\mathrm{900}\right] \\ $$$${use}\:{of}\:\mathrm{0}\:{in}\:{this}\:\mathrm{9}\:{numbers}=\mathrm{9}×\mathrm{2}=\mathrm{18}\blacksquare \\ $$$$ \\ $$$${Three}\:\boldsymbol{{digit}}\:\boldsymbol{{no}}\:{tength}\:{place}\:\mathrm{0}\rightarrow{unit}\:{plac}\left(\mathrm{1}\:{to}\mathrm{9}\right)\rightarrow \\ $$$${hundred}\:{place}\:\rightarrow{any}\:{number}\:\left(\mathrm{1},\mathrm{2},\mathrm{3}..\mathrm{9}\right) \\ $$$$\mathrm{9}×\mathrm{1}×\mathrm{9}=\mathrm{81} \\ $$$${use}\:{of}\:\mathrm{0}\rightarrow\mathrm{1}×\mathrm{81}=\mathrm{81}\blacksquare \\ $$$$ \\ $$$$\left.\mathrm{4}\right){four}\:{dugit}\:{no} \\ $$$$\overset{×} {−}\:\:\overset{×} {−}\:\overset{×} {−}\:\overset{\mathrm{0}} {−}\rightarrow\mathrm{9}×\mathrm{9}×\mathrm{9}×\mathrm{1}=\mathrm{729} \\ $$$$\overset{×} {−}\:\overset{×} {−}\:\overset{\mathrm{0}} {−}\:\overset{×} {−}\rightarrow\mathrm{9}×\mathrm{9}×\mathrm{1}×\mathrm{9}=\mathrm{729} \\ $$$$\overset{×} {−}\:\overset{\mathrm{0}} {−}\:\overset{×} {−}\:\overset{×} {−}\rightarrow\mathrm{9}×\mathrm{1}×\mathrm{9}×\mathrm{9}=\mathrm{729} \\ $$$$\overset{×} {−}\:\overset{×} {−}\:\overset{\mathrm{0}} {−}\:\overset{\mathrm{0}} {−}\rightarrow\mathrm{9}×\mathrm{9}×\mathrm{1}×\mathrm{1}=\mathrm{81} \\ $$$$\overset{×} {−}\:\overset{\mathrm{0}} {−}\overset{×} {−}\:\overset{\mathrm{0}} {−}\rightarrow\mathrm{9}×\mathrm{1}×\mathrm{9}×\mathrm{1}=\mathrm{81} \\ $$$$\overset{×} {−}\:\overset{\mathrm{0}} {−}\:\overset{\mathrm{0}} {−}\:\overset{×} {−}\rightarrow\mathrm{9}×\mathrm{1}×\mathrm{1}×\mathrm{9}=\mathrm{81} \\ $$$${use}\:{of}\:\mathrm{0}\:\left[\mathrm{729}+\mathrm{729}+\mathrm{729}\right]×\mathrm{1}\blacksquare \\ $$$${use}\:{of}\:\mathrm{00}\left[\mathrm{81}+\mathrm{81}+\mathrm{81}\right]×\mathrm{2}\blacksquare \\ $$$$ \\ $$$$\overset{×} {−}\overset{\mathrm{0}} {−}\:\:\overset{\mathrm{0}} {−}\overset{\mathrm{0}} {−}\:\rightarrow\mathrm{9}×\mathrm{1}×\mathrm{1}×\mathrm{1}=\mathrm{9} \\ $$$${use}\:{of}\:\mathrm{000}=\mathrm{9}×\mathrm{3}=\mathrm{27}\blacksquare \\ $$$$\boldsymbol{{sir}}\:\boldsymbol{{pls}}\:\boldsymbol{{check}}\:\boldsymbol{{till}}\:\boldsymbol{{now}}\:\boldsymbol{{to}}\:\boldsymbol{{get}}\:\boldsymbol{{the}}\:\boldsymbol{{use}}\:\boldsymbol{{of}}\:\mathrm{0} \\ $$$$\boldsymbol{{we}}\:\boldsymbol{{have}}\:\boldsymbol{{to}}\:\boldsymbol{{add}}\:\blacksquare\:{marked}\:{value}… \\ $$$${pls}\:{check}.. \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{have}}\:\boldsymbol{{cslculated}}\:\boldsymbol{{only}}\:\boldsymbol{{use}}\:\boldsymbol{{of}}\:\mathrm{0}\:\boldsymbol{{till}}\:\boldsymbol{{now}}.. \\ $$$$ \\ $$
Commented by mr W last updated on 27/Jan/19
correct sir!
$${correct}\:{sir}! \\ $$
Commented by Otchere Abdullai last updated on 27/Jan/19
Brilliant
$${Brilliant} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19
thank you sir for your kind perusal through it..  now i shall try to solve for 1...
$${thank}\:{you}\:{sir}\:{for}\:{your}\:{kind}\:{perusal}\:{through}\:{it}.. \\ $$$${now}\:{i}\:{shall}\:{try}\:{to}\:{solve}\:{for}\:\mathrm{1}… \\ $$
Commented by Tawa1 last updated on 28/Jan/19
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *