Puzzle #41: toilet rolls during lockdown

It’s lockdown and you have run out of toilet rolls.

Since stock are low, supermarkets have decided to apply the following special rules to the sales of toilet rolls.

• only 1 shopper is allowed in the shop at any time
• at the entrance of each supermarket a sticker will be attached to the back of each shopper
• the sticker is black or white
• each shopper cannot see its own sticker
• every shopper can buy only one box of toilet rolls and can go to the shop only once per week
• once finished with the shopping, each shopper must build up a queue in front of till to check out. At this point a new shopper can enter in the shop
• while the queue is building up, each shopper can see the sticker of all the shoppers in front of him/her (example: the first shopper cannot see anything, the second shopper can see the first shopper sticker only, …, the last shopper can see all shoppers stickers)
• while in the queue, shoppers cannot turn or communicate in any form
• as soon as there are 20 shoppers in the queue, starting form the last shopper in the queue, the supermarket shop assistant asks the shopper to guess the colour of its own sticker. The shopper must say loudly a colour: if the shopper says the correct colour then he/she can buy the toilet rolls otherwise he/she needs to leave the shop without any rolls. After this the shopper will go away without been seen by the other shoppers
• the shop assistant move to the penultimate shopper and ask the same question and this goes on until the first shopper

Your partner is putting pressure on you: you must buy the toilet rolls asap! You decide to create a nextdoor group to discuss a plan to maximise the chances to get a box of toilet rolls. In 2 hours your group reach 20 members.

What is the best strategy to maximize the number of toilet rolls that your group can buy?

Have fun!