Mr. P uses an insulin pen to help manage his diabetes. Each pen is filled with 3 ml of insulin or 300 units.
Each time that he uses the pen he must first "prime" it by draining off 2 units.
Then he injects 12 units of insulin into his system on one day and 13 units the next, always alternating 12 units and then 13 units.
When there are less than 14 units (on the 12 unit days) or less than 15 units (on the 13 unit days), Mr. P must prime the current pen and then
prime the new pen just to get a total of one dose of insulin.
How many insulin pens must Mr. P go through before the insulin comes out evenly? (in other words, there is no insulin left in the pen when
he finishes that day's dose of insulin).
Solution to the Problem:
It would take seven pens until there was no insulin left in the pen when Mr. P finished his daily dose of insulin.PEN #1:
10 days of 12 units = 140
10 days of 13 units = 150
Remaining 10 units: 2 prime, 8 units
PEN #2:
Finish 2 prime, 4 units = 6
10 days of 13 units = 150
10 days of 12 units = 140
Remaining 4 units: 2 prime, 2 units
PEN #3:
Finish 2 prime, 11 units = 13
10 days of 12 units = 140
9 days of 13 units = 135
Remaining 12 units: 2 prime, 10 units
PEN #4:
Finish 2 prime, 3 units = 5
10 days of 12 units = 140
10 days of 13 units = 150
Remaining 5 units: 2 prime, 3 units
PEN #5:
Finish 2 prime, 9 units = 11
9 days of 12 units = 126
10 days of 13 units = 150
Remaining 13 units: 2 prime, 11 units
PEN #6:
Finish 2 prime, 1 units = 3
10 days of 12 units = 140
10 days of 13 units = 150
Remaining 7 units: 2 prime, 5 units
PEN #7:
Finish 2 prime, 8 units = 10
10 days of 12 units = 140
10 days of 13 units = 150
No remaining units
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Rob Miles | Northbrook, Illinois |
| 3. Ivy Joseph | Pune, Maharashtra, India |
| 4. Nakoda Bird |
Mountain View High School, Mountain View, Wyoming |