### Brain Teasers

# 861 Candles

I have always had the correct number of candles on each of my birthday cakes. I have had exactly one birthday cake for each year of my life. If I have blown out a total of 861 candles thus far, how old am I?

Can you find the answer without just adding up numbers until you reach 861?

Can you find the answer without just adding up numbers until you reach 861?

### Hint

1+ 2+ 3 + ... + n = 861 .To sum up the first n positive integers, the following formula is helpful:

Sum = n*(n+1)/2

Think of it this way: find the smaller of two consecutive positive integers such that half the product of the integers is 861.

### Answer

41If n = 41 , we see that:

S = 41(41+1)/2 = 41(42)/2 = 861.

Thus, if you add up the integers from 1 to 41, you will get a total of 861.

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