Ten-balls-were-manufactured-nine-of-them-have-the-same-mass-while-just-one-of-them-has-a-slightly-higher-or-slightly-lower-mass-Given-is-just-a-beam-balance-and-no-weights-comparing-the-masses-of

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Question Number 16450 by ajfour last updated on 22/Jun/17

$$Tenballsweremanufactured,$$$$nineofthemhavethesame$$$$mass,whilejustoneofthem$$$$hasaslightlyhigherorslightly$$$$lowermass.Givenisjustabeam$$$$balanceandnoweights.comparing$$$$themassesofballsonly,withthe$$$$helpofthebalance,andinjust$$$$3weighingsexplainhowtojudge$$$$whichisthedefectiveoneand$$$$whetheritisheavierorlighter$$$$thantherest\left(asthecasemaybe\right).$$

Commented by prakash jain last updated on 22/Jun/17

$$10\mathrm{balls}=b_1,\dots ,b_{10}$$$$set\mathrm{A}=b_1,b_2,b_3$$$$setB=b_4,b_5,b_6$$$$setC=b_7,b_8,b_9$$$$2\mathrm{weighs}\mathrm{compare}\mathrm{A}\mathrm{\&}\mathrm{B}\mathrm{and}\mathrm{A}\mathrm{\&}\mathrm{C}$$$$\mathrm{case}1:\mathrm{A}=\mathrm{B}=\mathrm{C}$$$$b_{10}\mathrm{is}\mathrm{fault}.$$$$\mathrm{measure}{b}_{10}\mathrm{with}{b}_1\mathrm{to}\mathrm{find}\mathrm{out}$$$$\mathrm{if}{b}_{10}\mathrm{is}\mathrm{heavier}\mathrm{to}\mathrm{lighter}.$$$$\mathrm{case}2:\mathrm{one}\mathrm{of}\mathrm{group}\mathrm{is}\mathrm{unequal}$$$$\mathrm{at}\mathrm{we}\mathrm{know}\mathrm{the}\mathrm{defective}\mathrm{set}$$$$\mathrm{and}\mathrm{whether}\mathrm{it}\mathrm{is}\mathrm{heavier}\mathrm{to}\mathrm{lighter}$$$$\mathrm{than}\mathrm{the}\mathrm{other}.\mathrm{Let}\mathrm{us}\mathrm{say}\mathrm{set}\mathrm{is}\mathrm{A}.$$$$\mathrm{compare}{b}_1\mathrm{and}{b}_2\mathrm{if}\mathrm{equal}{b}_3\mathrm{is}\mathrm{defectivd}$$$$\mathrm{if}\mathrm{equal}{b}_3\mathrm{is}\mathrm{defectivd}$$$$\mathrm{if}\mathrm{not}\mathrm{equal}\mathrm{the}\mathrm{heavier}\mathrm{or}\mathrm{lighter}$$$$\mathrm{ball}\mathrm{is}\mathrm{defective}.(\mathrm{we}\mathrm{already}$$$$\mathrm{identified}\mathrm{the}\mathrm{nature}\mathrm{of}\mathrm{defecr})$$

Commented by prakash jain last updated on 22/Jun/17

$$\mathrm{Extension}:\mathrm{How}\mathrm{many}\mathrm{measurement}\mathrm{are}\mathrm{required}$$$$\mathrm{if}\mathrm{there}\mathrm{are}3n+1\mathrm{balls}\mathrm{and}$$$$1\mathrm{is}\mathrm{defective}.$$

Commented by ajfour last updated on 23/Jun/17

$$Greatsolvingsir,goodnoticing$$$$ability.Thanks.$$

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