The Giant's Boots
If Tamanda just happened to pull out his 16 size-22 boots, and his 14 size-21 boots, he still would not have one boot of each. If Tamanda pulls out 31 boots, he will be sure of having at least one pair.
We had several budding mathmeticians submit solutions to this week's question. Among them was this one from Johnathan Loerchner and Reegan Price (Grade 8):
Answer =(8x2)+(7x2)+1 =16+14+1 =30+1 =31Henceforth the amount of boots Tamanda would have to pull out of the closet to be sure of having one of each size would be 31.
Ian MacLennan gave us this wonderfully clear and detailed explanation:
If he needs one of each boot(not a pair):
There would be 16 size 22 boots, 14 size 21 boots and 12 size 20 boots. In the worst possible case, he could pull out all of the size 22 boots (16), and then all of the size 21 boots (14) and then there would only be size 20 boots left in the closet. He would need to pull out one more to have at least one of each size. 16 + 14 + 1 = 31 boots. He would have to pull out 31 boots to make sure he had one boot of each size.
At the end of the process, he would have a jumble of boots outside of his closet instead of a jumble of boots inside the closet.
And finally, Ashley Campbell of Ottawa, Ontario tells us:
I think the answer is 31 boots to be certain he had one of each boot.