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Question Number 95846 by naka3546 last updated on 28/May/20

$$A=\{0,1,2,3,...,2020\}$$$$howmanyzeroonA?$$

Answered by Rasheed.Sindhi last updated on 28/May/20

$${}^{\prime }{\mathrm{\_}}^{\prime }\mathrm{is}\mathrm{nonzero}\mathrm{digit}\mathrm{in}\mathrm{the}\mathrm{following}.$$$$1-\mathrm{digit}\mathrm{numbers}:$$$$0:1\times 1=1\left(1zero\right)$$$$2-\mathrm{digit}\mathrm{numbers}:$$$$\mathrm{\_}0:9\times 1=9$$$$3-\mathrm{digit}\mathrm{numbers}:$$$$\mathrm{\_}\mathrm{\_}0:9\times 9\times 1=81\times 1=81$$$$\mathrm{\_}0\mathrm{\_}:9\times 1\times 9=81\times 1=81$$$$\mathrm{\_}00:9\times 1\times 1=9\times 2=18$$$$4-\mathrm{digit}\mathrm{numbers}:$$$$Singlezero$$$$1\mathrm{\_}\mathrm{\_}0:1\times 9\times 9\times 1=81$$$$1\mathrm{\_}0\mathrm{\_}:1\times 9\times 1\times 9=81$$$$10\mathrm{\_}\mathrm{\_}:1\times 1\times 9\times 9=81$$$$2\mathrm{\_}\mathrm{\_}0:1\times 0\times 2\times 1=0$$$$2\mathrm{\_}0\mathrm{\_}:1\times 0\times 1\times 9=0$$$$201\mathrm{\_}:1\times 1\times 1\times 9=9$$$$202\mathrm{\_}:1\times 1\times 1\times 0=0$$$$\{81\times 3+9\}\times 1=252$$$$$$$$Doublezeros$$$$10\mathrm{\_}0:1\times 1\times 9\times 1=9$$$$100\mathrm{\_}:1\times 1\times 1\times 9=9$$$$1\mathrm{\_}00:1\times 9\times 1\times 1=9$$$$20\mathrm{\_}0:1\times 1\times 2\times 1=2$$$$200\mathrm{\_}:1\times 1\times 1\times 9=9$$$$2\mathrm{\_}00:2\times 0\times 1\times 1=0$$$$(9\times 4+2)\times 2=76$$$$Triplezeros$$$$1000:=1\times 3=3$$$$2000:=1\times 3=3$$$$6$$$$Answer:524$$$$Pleaseconfirm.$$

Commented by naka3546 last updated on 22/Jun/20

$$Thankyou,sir.{It}^{\prime }scorrect.$$

Commented by Rasheed.Sindhi last updated on 22/Jun/20

$${You}^{\prime }rewelcomesir!$$

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