There are 240 injections in a laboratory. Only one injection contains an anaesthetic. You have 5 rats to find which injection is the anaesthetic. You must solve this within 48 hours.
Rules:
- If a rat is given an anaesthetic injection, it will become faint(unconscious) within 24 hours.
- Once a rat becomes unconscious, it cannot be used again.
- A rat can be given more than one injection (at different times) until it becomes unconscious.
How can you use the 5 rats to find the exact anaesthetic injection within 48 hours?
Check if you were right - full answer with solution below.
Solution:
Let us number each injection with unique 5-digit numbers consisting of only 0, 1, and 2.
Let us number the Rats as 1, 10, 100, 1000, 10000.
- The action corresponding to the digit in the unit place will be executed by rat numbered 1.
- The action corresponding to the digit in the tenth place will be executed by rat numbered 10.
- The action corresponding to the digit in the 100th place will be executed by rat numbered 100.
- The action corresponding to the digit in the 1000th place will be executed by rat numbered 1000.
- The action corresponding to the digit in the 10000th place will be executed by rat numbered 10000.
Number meanings on an injection:
- Number 0 on an Injection represents that the injection will not be injected to the rat.
- Number 1 on an Injection represents that the injection will be injected to the rat on the 1st day.
- Number 2 on an Injection represents that the injection will be injected to the rat on the 2nd day (after 24 hours).
Example:
Let us say the Injection is numbered 11201. The Injections is injected on the first day to rat numbered 10000, 1000, and 1. It is injected on the second day to rat numbered 100. And it is not injected to rat numbered 10.
So if the rats numbered 10000, 1000 and 1 faint within first 24 hours, rat numbered 100 faints in the next 24 hours and the rat numbered 10 does not faint, then the Anesthesia Injection has to be 11201.
Total number of injections that can be tested in this way will be:
= 3 * 3 * 3 * 3 * 3 = 3^5 = 243 Injections
So with the help of 5 rats and within 48 hours we will be able to find a Anesthesia Injection among 243 Injections.