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Question Number 156462 by MathSh last updated on 11/Oct/21

$$\mathrm{If}\overline{\mathrm{abc}}=\overline{\mathrm{cba}}+\overline{\mathrm{def}}\mathrm{and}\mathrm{a}\in \{\mathrm{c}+2;...;9\}$$$$\mathrm{Then}\mathrm{find}\overline{\mathrm{def}}+\overline{\mathrm{fed}}$$$$$$

Answered by Rasheed.Sindhi last updated on 11/Oct/21

$$$$$$\mathrm{let}\mathrm{c}=1\Rightarrow \mathrm{a}\in \{3,4,...,9\}$$$$\mathrm{a}=3:$$$$\overline{3\mathrm{b}1}=\overline{1\mathrm{b}3}+\overline{\mathrm{def}}$$$$\overline{\mathrm{def}}=\overline{3\mathrm{b}1}-\overline{1\mathrm{b}3}=301-103=198$$$$\overline{\mathrm{def}}=198\Rightarrow \overline{\mathrm{fed}}=891$$$$\overline{\mathrm{def}}+\overline{\mathrm{fed}}=198+891=1089$$

Commented by MathSh last updated on 11/Oct/21

$$\mathrm{Yes},\mathrm{thank}\mathrm{you}\mathrm{dear}\mathbf{S}\mathrm{er},\mathrm{similary}$$$$297\to 792;396\to 693;495\to 594...$$

Commented by Rasheed.Sindhi last updated on 11/Oct/21

$$\mathrm{Of}\mathrm{course}!\mathrm{we}\mathrm{can}\mathrm{show}\mathrm{that},\mathrm{in}\mathrm{general}$$$$\mathrm{way}\mathrm{also}.$$

Commented by MathSh last updated on 11/Oct/21

$$\mathrm{Yes}\mathrm{my}\mathrm{dear}\mathbf{S}\mathrm{er},\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}$$

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