Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 183664 by Rasheed.Sindhi last updated on 28/Dec/22

How many artificially made weights are required (minimally) to weigh ONLY 1,3,5,...,79 kg and what should be they?

$$ \\ $$$$\mathcal{H}{ow}\:{many}\:{artificially}\:{made}\:{weights}\:{are}\: \\ $$$$\boldsymbol{{required}}\:\left({minimally}\right)\:{to}\:{weigh} \\ $$$$\:\underline{\mathrm{ONLY}}\:\:\:\:\:\mathrm{1},\mathrm{3},\mathrm{5},...,\mathrm{79}\:{kg}\: \\ $$$${and}\:{what}\:{should}\:{be}\:{they}? \\ $$

Commented by Frix last updated on 28/Dec/22

The problem might be this: If we want to weigh only 1, 3 kg we need • 1 and 3 but then we also get 2 and 4 • 1 and 2 but then we also get 2 • 1 and 4 but then we also get 4 and 5 • .5 and 2.5 ... ⇒ I think there′s no solution

$$\mathrm{The}\:\mathrm{problem}\:\mathrm{might}\:\mathrm{be}\:\mathrm{this}: \\ $$$$\mathrm{If}\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{weigh}\:{only}\:\mathrm{1},\:\mathrm{3}\:\mathrm{kg}\:\mathrm{we}\:\mathrm{need} \\ $$$$\bullet\:\mathrm{1}\:\mathrm{and}\:\mathrm{3}\:\mathrm{but}\:\mathrm{then}\:\mathrm{we}\:\mathrm{also}\:\mathrm{get}\:\mathrm{2}\:\mathrm{and}\:\mathrm{4} \\ $$$$\bullet\:\mathrm{1}\:\mathrm{and}\:\mathrm{2}\:\mathrm{but}\:\mathrm{then}\:\mathrm{we}\:\mathrm{also}\:\mathrm{get}\:\mathrm{2} \\ $$$$\bullet\:\mathrm{1}\:\mathrm{and}\:\mathrm{4}\:\mathrm{but}\:\mathrm{then}\:\mathrm{we}\:\mathrm{also}\:\mathrm{get}\:\mathrm{4}\:\mathrm{and}\:\mathrm{5} \\ $$$$\bullet\:.\mathrm{5}\:\mathrm{and}\:\mathrm{2}.\mathrm{5}\:... \\ $$$$\Rightarrow\:\mathrm{I}\:\mathrm{think}\:\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{solution} \\ $$

Commented by Rasheed.Sindhi last updated on 29/Dec/22

ThanX Frix sir! very right are you... In case we release the only condition has the question unique solution then? See Q#183646

$$\mathbb{T}\boldsymbol{\mathrm{han}}\mathbb{X}\:\mathrm{Frix}\:\mathrm{sir}!\:{very}\:{right}\:{are}\:{you}... \\ $$$${In}\:{case}\:{we}\:{release}\:{the}\:\underline{\mathrm{only}}\:{condition} \\ $$$${has}\:{the}\:{question}\:\:\mathrm{unique}\:{solution} \\ $$$${then}?\:{See}\:{Q}#\mathrm{183646} \\ $$

Commented by mr W last updated on 29/Dec/22

to weigh only 1,3,5,...,79 kg, there is no solution. to weigh not only 1,3,5,...,79 kg,we need at least 5 weights. with 5 weights there are at least two solutions: 1,3,9,27,81 or 1,2,6,18,54.

$${to}\:{weigh}\:{only}\:\mathrm{1},\mathrm{3},\mathrm{5},...,\mathrm{79}\:{kg},\:{there}\:{is} \\ $$$${no}\:{solution}. \\ $$$${to}\:{weigh}\:{not}\:{only}\:\mathrm{1},\mathrm{3},\mathrm{5},...,\mathrm{79}\:{kg},{we} \\ $$$${need}\:{at}\:{least}\:\mathrm{5}\:{weights}.\:{with}\:\mathrm{5}\:{weights} \\ $$$${there}\:{are}\:{at}\:{least}\:{two}\:{solutions}: \\ $$$$\mathrm{1},\mathrm{3},\mathrm{9},\mathrm{27},\mathrm{81}\:{or} \\ $$$$\mathrm{1},\mathrm{2},\mathrm{6},\mathrm{18},\mathrm{54}. \\ $$

Commented by Rasheed.Sindhi last updated on 29/Dec/22

∨ ∩i⊂∈ sir! ThanX!

$$\vee\:\cap\boldsymbol{\mathrm{i}}\subset\in\:\boldsymbol{\mathrm{sir}}!\:\:\mathcal{T}{han}\mathcal{X}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com