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Question Number 206353 by BaliramKumar last updated on 12/Apr/24

Commented by Rasheed.Sindhi last updated on 15/Apr/24

I think 15 is wrong here, it should be 14 or otherwise the answer is not correct.

$${I}\:{think}\:\mathrm{15}\:{is}\:{wrong}\:{here},\:{it}\:{should} \\ $$$${be}\:\mathrm{14}\:{or}\:{otherwise}\:{the}\:{answer}\:{is} \\ $$$${not}\:{correct}. \\ $$

Commented by Rasheed.Sindhi last updated on 15/Apr/24

PLEASE response.

$$\mathrm{PLEASE}\:\mathrm{response}. \\ $$

Commented by BaliramKumar last updated on 15/Apr/24

This is solution i am no under stand

$$\mathrm{This}\:\mathrm{is}\:\mathrm{solution}\: \\ $$$$\mathrm{i}\:\mathrm{am}\:\mathrm{no}\:\mathrm{under}\:\mathrm{stand} \\ $$

Commented by BaliramKumar last updated on 15/Apr/24

Commented by Rasheed.Sindhi last updated on 15/Apr/24

•Very poor ′physical health′ of the solution! I ′ll try its better version below. •Coudn′t say about ′mental health′ i-e ′logical fitness′ of the solution. (There are many exerts for this) albeit I′ll give my own understanding about the question, although after reposting it.

$$\bullet{Very}\:{poor}\:'{physical}\:{health}'\:{of} \\ $$$$\:\:\:{the}\:{solution}!\:\mathcal{I}\:'{ll}\:{try}\:{its}\:{better} \\ $$$$\:\:\:{version}\:{below}. \\ $$$$\bullet{Coudn}'{t}\:{say}\:{about}\:'{mental}\:{health}' \\ $$$$\:\:{i}-{e}\:\:'{logical}\:{fitness}'\:{of}\:{the}\:{solution}. \\ $$$$\:\:\:\left(\mathcal{T}{here}\:{are}\:{many}\:{exerts}\:{for}\:{this}\right) \\ $$$$\:\:\:{albeit}\:{I}'{ll}\:{give}\:{my}\:{own}\:{understanding}\: \\ $$$$\:\:\:{about}\:{the}\:{question},\:{although}\:{after}\: \\ $$$$\:\:\:{reposting}\:{it}. \\ $$

Commented by Rasheed.Sindhi last updated on 15/Apr/24

14.(2) Number of soldiers standing in the hollow square with depth of 8,10,12 or 15=4×lcm(8,10, 12,15) because they will stand on the perimeter of the square only...least common multiple of 8,10,12 and 15 : 2 ∣8 ,10, 12, 15 2 ∣4, 5, 6, 15 3 ∣2, 5, 3, 15 5 ∣2, 5, 1, 5 2, 1, 1, 1 ...LS= 2×2×3×5×2=120 The total number required in the hollow square =4×4×30 But at least the number of soldiers standing in a solid square =4×4×30×30=14400

$$\mathrm{14}.\left(\mathrm{2}\right)\:{Number}\:{of}\:{soldiers}\:{standing} \\ $$$$\:\:\:\:\:{in}\:{the}\:{hollow}\:{square}\:{with}\:{depth} \\ $$$$\:\:\:\:\:{of}\:\mathrm{8},\mathrm{10},\mathrm{12}\:{or}\:\mathrm{15}=\mathrm{4}×{lcm}\left(\mathrm{8},\mathrm{10},\right. \\ $$$$\left.\:\:\:\:\mathrm{12},\mathrm{15}\right)\:{because}\:{they}\:{will}\:{stand} \\ $$$$\:\:\:\:{on}\:{the}\:{perimeter}\:{of}\:{the}\:{square} \\ $$$$\:\:\:\:{only}...{least}\:{common}\:{multiple}\: \\ $$$$\:\:\:{of}\:\mathrm{8},\mathrm{10},\mathrm{12}\:{and}\:\mathrm{15}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\:\underline{\mid\mathrm{8}\:,\mathrm{10},\:\mathrm{12},\:\mathrm{15}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\:\underline{\mid\mathrm{4},\:\:\:\mathrm{5},\:\:\:\:\mathrm{6},\:\:\mathrm{15}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{3}\:\underline{\mid\mathrm{2},\:\:\:\mathrm{5},\:\:\:\:\mathrm{3},\:\:\mathrm{15}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{5}\:\underline{\mid\mathrm{2},\:\:\:\mathrm{5},\:\:\:\:\mathrm{1},\:\:\:\:\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2},\:\:\:\:\mathrm{1},\:\:\:\:\mathrm{1},\:\:\:\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:...{LS}=\:\mathrm{2}×\mathrm{2}×\mathrm{3}×\mathrm{5}×\mathrm{2}=\mathrm{120} \\ $$$$\:\mathcal{T}{he}\:{total}\:{number}\:{required}\:{in}\:{the}\:{hollow}\:{square} \\ $$$$\:\:\:\:\:=\mathrm{4}×\mathrm{4}×\mathrm{30} \\ $$$${But}\:{at}\:{least}\:{the}\:{number}\:{of}\:{soldiers} \\ $$$${standing}\:{in}\:{a}\:{solid}\:{square} \\ $$$$\:\:\:\:=\mathrm{4}×\mathrm{4}×\mathrm{30}×\mathrm{30}=\mathrm{14400} \\ $$

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