The Core 4:
22LR
223
30-06
458 Win Mag
With those 4 I'd feel comfortable hunting anything. But since you asked for 7:
32-20
260 Rem
338 Win Mag
This would result in the following battery:
22LR small game
32-20 larger small game
223 varmints
260 Rem light carbine for light big game
30-06 full size rifle for big game
338 Win Mag full size rifle for BIG game
458 Win Mag full size rifle for dangerous game
Not much you can't hunt with that group.
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