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Question Number 36844 by tawa tawa last updated on 06/Jun/18

$$\mathrm{find}\mathrm{the}\mathrm{sum}\mathrm{of}4\mathrm{digit}\mathrm{even}\mathrm{numbers}\mathrm{formed}\mathrm{from}\mathrm{the}\mathrm{digit}1,2,3,4$$

Answered by MJS last updated on 06/Jun/18

$$4\times 4\times 4\times 2=128\mathrm{even}\mathrm{numbers}$$$$64\mathrm{abc}2$$$$64\mathrm{abc}4$$$$$$$$32\mathrm{ab}1\mathrm{c}$$$$32\mathrm{ab}2\mathrm{c}$$$$...$$$$$$$$32(1000+2000+3000+4000)=320000$$$$32(100+200+300+400)=32000$$$$32(10+20+30+40)=3200$$$$64(2+4)=384$$$$$$$$\mathrm{sum}=355584$$

Commented by Rasheed.Sindhi last updated on 06/Jun/18

$$\mathcal{N}iceSir!$$

Commented by tawa tawa last updated on 06/Jun/18

$$\mathrm{please}\mathrm{what}\mathrm{is}32\mathrm{ab}1\mathrm{c}\mathrm{etc}.\mathrm{from}\mathrm{your}\mathrm{solution}.\mathrm{i}\mathrm{can}\mathrm{see}\mathrm{that}\mathrm{numbers}\mathrm{that}$$$$\mathrm{end}\mathrm{with}2\mathrm{is}64,\mathrm{numbers}\mathrm{that}\mathrm{end}\mathrm{with}4\mathrm{is}64.\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{the}32\mathrm{ab}1\mathrm{c}\mathrm{etc}$$$$\mathrm{thanks}.\mathrm{please}\mathrm{explain}$$

Commented by tawa tawa last updated on 06/Jun/18

$$\mathrm{And}\mathrm{what}\mathrm{if}\mathrm{repetition}\mathrm{of}\mathrm{digit}\mathrm{is}\mathrm{not}\mathrm{allowed}$$

Commented by tawa tawa last updated on 06/Jun/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by MJS last updated on 06/Jun/18

$$abc\mathrm{stand}\mathrm{for}\mathrm{any}\mathrm{combination}\mathrm{of}1,2,3,4$$$$\mathrm{we}\mathrm{have}128\mathrm{numbers},\mathrm{each}32\mathrm{start}\mathrm{with}$$$$1000,2000,3000,4000,\mathrm{each}32\mathrm{contain}$$$$100,200,300,400,\mathrm{each}32\mathrm{contain}10,20,30,40$$$$$$$$\mathrm{if}\mathrm{no}\mathrm{repetition}\mathrm{is}\mathrm{allowed}:$$$$1234,1324,2134,2314,3124,3214$$$$1342,1432,3142,3412,4132,4312$$$$\mathrm{sum}=31116$$

Commented by tawa tawa last updated on 06/Jun/18

$$\mathrm{can}\mathrm{we}\mathrm{get}\mathrm{that}31116\mathrm{by}\mathrm{calculation}?.\mathrm{i}\mathrm{used}\mathrm{your}\mathrm{method}\mathrm{above}.\mathrm{am}\mathrm{not}$$$$\mathrm{getting}31116.$$$$$$$$\mathrm{i}\mathrm{appreciate}\mathrm{your}\mathrm{effort}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by MJS last updated on 06/Jun/18

$$4\times 1000+2\times 2000+4\times 3000+2\times 4000=28000$$$$4\times 100\times 2\times 200+4\times 300+2\times 400=2800$$$$4\times 10+2\times 20+4\times 30+2\times 40=280$$$$6\times 2+6\times 4=36$$$$28000+2800+280+36=31116$$

Commented by tawa tawa last updated on 06/Jun/18

$$\mathrm{wow}\mathrm{great}\mathrm{but}\mathrm{i}\mathrm{dont}\mathrm{really}\mathrm{understand}.\mathrm{i}\mathrm{want}\mathrm{to}\mathrm{understand}\mathrm{so}\mathrm{that}\mathrm{i}\mathrm{can}\mathrm{know}$$$$\mathrm{it}\mathrm{because}\mathrm{of}\mathrm{exam}$$

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