Question

Suppose seven pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair

Answer 1

Answer:

8 individual boots must be picked to be sure of getting a matched pair.

Step-by-step explanation:

Step 1: Using the pigeonhole principle.

The pidgeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

A good illustration of the pigeonhole principle is the number of gloves one can have. For example, if one has three gloves, then one must have at least two right-hand gloves, or at least two left-hand gloves, because one has three objects, but only either a left hand or a right, two options of handedness to put on the gloves. Thus the third glove must be a pair of either the right-hand or left-hand glove

Step 2: Determining n and m

Since there are 7 pairs of boots, there will be 7 × 2 individual boots; n = 7

Now since there cannot be more than 7 pairs of the boot, m = 7

Step 3: Determining the minimum number of individual boots that must be picked in order to get a pair.

After all the 7 individual boots have been picked, the next individual boot picked must be a pair of one of the 7 boots picked. Thus, 7 + 1 = 8 individual boots must be picked to be sure of getting a matched pair.