# Finger Lickin’ Good

A father bought a KFC special custom-made bucket of chicken and wanted to distribute the chicken pieces to his sons. To his eldest he gave one piece plus 1/7 of the remaining pieces; to his second eldest, two pieces plus 1/7 of the remaining pieces. To the third son, he gave three pieces plus 1/7 of remaining pieces and so on and so forth. All the pieces were distributed among his sons without remainder. How many sons and how many pieces were there in the KFC special custom made bucket chicken??

### 4 guesses to Finger Lickin’ Good

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• nikki

7 Sons and 35 bits of chicken

• Dude

Close … but no drumstick!

Keep trying.

• Golly Kim

6 Sons and 36 pieces.

• Dude

Golly Kim, you are correct!

After the eldest takes the first piece, the number of pieces must be a multiple of 7. (1st distribution).
After the eldest takes his 1/7th and the second eldest takes two pieces, the number of pieces must again be a multiple of 7. (2nd distribution).
Therefore, to go from the first and second distribution, we move from a multiple of 7 to another multiple of 7. The easiest way to do this is to take away 7 pieces.
Then the eldest’s 1/7th plus the second eldest’s 2 pieces must equal 7.
Therefore, the eldest’s 1/7th must equal five since 5 + 2 = 7.
If 1/7th is 5, 7/7ths is 35.

Add the drumstick that the eldest first took, and you find a total of 36 pieces.
Work through the problem, and you find six sons.

You are today’s winner.