Page 38 - NUMINO Challenge_D2
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Basic Concepts Unlock the Door
If there are three locked doors and three
different keys as shown on the right, the
following two ways show how to find all
three doors in order from door 1.
The luckiest case will be unlocking
each door on the first try. In this case, 1 1 1 3 (tries) will unlock all three
doors.
The worst case will be unlocking each door on the last try. This means that
three tries will unlock door 1, two tries will unlock door 2, and one try will
unlock door three. In this case, 3 2 1 6 (tries) will unlock all three doors.
Therefore, you need to try at least six times to unlock all three doors.
Example There are five locked drawers and five different keys. At least how
many times do you need to try in order to find the matching keys
for all five drawers?
Class Notes
Use one key at a time to find the matching key for drawer 1. If four of the five keys
do not unlock the drawer, the last key will match drawer 1. Therefore, you need to
try at least times.
Use the rest of the four keys in order to find the matching key for drawer 2. By using
the method shown above, you need to try at least times because when the first
three keys do not unlock the drawer, the last key will match drawer 2.
By using the same method, you need to try at least times to find the matching
key for drawer 3 and times to find the matching key for drawer 4. You do not
need to unlock the last drawer because the last drawer will match the last key.
Therefore, you need to try at least 4 3 2 1 (times) to find the matching keys
for all five drawers.
Try It Again There are five stamps for ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’ that are not
arranged in order. At least how many times does Lisa need to
stamp a paper to make the order of ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’
without looking at the bottom of the stamps?
35Reasoning
If there are three locked doors and three
different keys as shown on the right, the
following two ways show how to find all
three doors in order from door 1.
The luckiest case will be unlocking
each door on the first try. In this case, 1 1 1 3 (tries) will unlock all three
doors.
The worst case will be unlocking each door on the last try. This means that
three tries will unlock door 1, two tries will unlock door 2, and one try will
unlock door three. In this case, 3 2 1 6 (tries) will unlock all three doors.
Therefore, you need to try at least six times to unlock all three doors.
Example There are five locked drawers and five different keys. At least how
many times do you need to try in order to find the matching keys
for all five drawers?
Class Notes
Use one key at a time to find the matching key for drawer 1. If four of the five keys
do not unlock the drawer, the last key will match drawer 1. Therefore, you need to
try at least times.
Use the rest of the four keys in order to find the matching key for drawer 2. By using
the method shown above, you need to try at least times because when the first
three keys do not unlock the drawer, the last key will match drawer 2.
By using the same method, you need to try at least times to find the matching
key for drawer 3 and times to find the matching key for drawer 4. You do not
need to unlock the last drawer because the last drawer will match the last key.
Therefore, you need to try at least 4 3 2 1 (times) to find the matching keys
for all five drawers.
Try It Again There are five stamps for ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’ that are not
arranged in order. At least how many times does Lisa need to
stamp a paper to make the order of ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’
without looking at the bottom of the stamps?
35Reasoning
