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Steps

Get all the supplies you need: all scimitars up to rune except for bronze, get full iron, strength amulet, and some food. (You might also want to get some decorations, like a Team-19 cape, gold gloves, and fancy boots. It looks really good.)
Train up to 3 strength in tutorial island (don’t train attack here).
Go to the goblins and get 8 strength (this may take a while).
Go to monks and train up to about 30 str strength and then raise to 3-5 attack.(Note* After you kill one, ask another to heal you, this way you need or use less food.)
Get 35 strength and 5 attack, and switch to steel scimitar.
Switch to Al Kharid warriors.
Get 45 strength and then 10 attack.
Raise your strength up to 55 strength and keep attack at 10.
Switch to scorpions next and get 65 strength and 15 attack.
Move on to level 2 Security Stronghold and train on those level 44 zombies. Train to 70 strength there and 25 attack (but at 20 attack move onto mithril scimitar).
Now you are at the perfect level to bh. Rely on bh to train strength for now on.
If you don’t want to rely on bh for your strength train on moss giants.
At No. 11/12, train your strength up to 80 and then 30 attack (use adamant scimitar).
Move on to lesers and get 90 strength and 40 attack (use the one you have been waiting for: rune scimitar)
Keep training at lessers, and eventually your hard work will pay off: you have 99 strength and 40 attack
Now go bh; you should dominate.
You can also get some friends around your level that are strength pures to help you kill other players in bh.

Tips

A very good weapon is the Talisman staff. You can put whichever talisman on it you like, and it gives +34 str bonus. You will need to completerune mysteries (an easy task) and get 50+ runecrafting (an easy, but maddeningly boring task)
When training on monks, you don’t have to worry about food, the monks can heal you.
Do not listen to those guides that say you should keep attack and strength at the same level. Those guides are wrong.
If somebody calls you a noob (NEW PLAYER) put him on ignore, and imagine what he looks like in real life and put him in a pool of sharks (I’m just being sarcastic but some people like that idea).
When pking try to use swordfish instead of lobsters.
The main point of pure strength is keep strength high and attack and defence low.
Avoid places like the chaos respawn as this is a clan hotspot and high levels will usually hide out there
Never fight a safer, you will MOST PROBABLY get killed by safers.
If they safe, you may want to safe too…

Warnings
Rangers can easily kill pure strength.