A local fast food chain sells chicken nuggets in three different sizes, with each size containing a different number of nuggets.
If it's impossible to buy 9 or 13 nuggets by mixing and matching sizes but possible to buy any number 14 or higher, what are the three sizes?
Solution:
There are many answers to this problem:
2, 4, and 15
2, 6, and 15
2, 8, and 15
2, 10, and 15
4, 7, and 10
4, 7, and 17
5, 7, and 11
With the three sizes, 4, 7, 17, the impossible number of nuggets to be bought are: 1, 2, 3, 5, 6, 9, 10, 13. All other number of nuggets can be bought.
For the sizes 5, 7, and 11,
Look at the table below:
| Total | Possible? | 5 | 7 | 11 |
|---|---|---|---|---|
| 1 | no | |||
| 2 | no | |||
| 3 | no | |||
| 4 | no | |||
| 5 | yes | 1 | ||
| 6 | no | |||
| 7 | yes | 1 | ||
| 8 | no | |||
| 9 | no | |||
| 10 | no | |||
| 11 | yes | 1 | ||
| 12 | no | |||
| 13 | no | |||
| 14 | yes | 2 | ||
| 15 | yes | 3 | ||
| 16 | yes | 1 | 1 | |
| 17 | yes | 2 | 1 | |
| 18 | yes | 1 | 1 | |
| 19 | yes | 1 | 2 | |
| 20 | yes | 4 | ||
| 21 | yes | 2 | 1 |
Once you find five numbers in a row that can be obtained (14 to 18 in this problem), you can get all numbers greater than 18 by adding a 5 to the numbers in that range.
The number 14 was obtained by ordering two 7's. the number 19 can be obtained by ordering one 5 and two 7's.
The number 15 was obtained by ordering three 5's. the number 20 can be obtained by ordering four 5's.
The number 16 was obtained by ordering one 5 and one 11. the number 21 can be obtained by two 5's and one 11.
Click here for another chicken nuggets problem
Click here for a similar problem from 7-11
Correctly solved by:
| 1. Kamal Lohia |
Holy Angel School, Hisar, Haryana, India |
| 2. Dr. Hari Kishan ** |
D.N. College, Meerut, Uttar Pradesh, India |
| 3. Ryan Hall |
Parkview Elementary, Chico, California, USA |
| 4. Davit Banana | Istanbul, Turkey |
| 5. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
** extra credit for sending in multiple answers