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# Math Competition Problems - Problem of the week - 2 (AMC8 Problem)

Updated: Apr 17, 2021

## Solution:

Since this is problem #9 in AMC 8, this should be relatively easy to solve and you should be able to solve it in under a minute. But a quick look will tell you that the arithmetic might take quite a bit of time. So what do we do?

Let's try listing it out

Day No. of widget sold Running total

1 1 1

2 3 4

3 5 9

4 7 16

5 9 25

......... and so on

Now that we have listed it out we can see a pattern.

The amount of widgets she sold on Day 1 is 1^2

The total no. of widgets she sold till Day 2 is 2^2

The total no. of widgets she sold till Day 3 is 3^2

The total no. of widgets she sold till Day 4 is 4^2

So the number of widgets she sold till Day n can be summed up by the expression n^2

So the total no. of widgets Janabel sold after working 20 days is 20^2 = 400.

This type of problem solving technique is called finding a pattern. Now try the following question on your own using the same technique and post your answers in the comments section below

"Each member of a club shook hands with every other member who came for a meeting. There were a total of 45 handshakes. How many members were present at the meeting?"

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