  We propose a novel method for producing very-neutron-rich hypernuclei and
corresponding resonance states by employing charge-exchange reactions via
pp($^{12}$C, $^{12}$N $K^+$)n$\Lambda$ with single-charge-exchange and
ppp($^{9}$Be, $^{9}$C $K^+$)nn$\Lambda$ with double-charge-exchange, both of
which produce $\Lambda K^+$ in a target nucleus. The feasibility of producing
very-neutron-rich hypernuclei using the proposed method was analysed by
applying an ultra-relativistic quantum molecular dynamics model to a
$^6$Li+$^{12}$C reaction at 2 $A$ GeV. The yields of very-neutron-rich
hypernuclei, signal-to-background ratios, and background contributions were
investigated. The proposed method is a powerful tool for studying
very-neutron-rich hypernuclei and resonance states with a hyperon for
experiments employing the Super-FRS facility at FAIR and HFRS facility at HIAF.
