Previous Problem:
This problem will take a few days to solve, so it is perfect for the holidays when you are looking for fun activities.
Consider the numbers 1 to 40, inclusive. Imagine trying to express each of those numbers as a combination of other numbers that are added or subtracted together – for example, 3 can be 1+2 or it can be 4-1.
Identify four numbers that, either singly or combination with some or all the other three numbers, can express every number from 1 to 40. In each combination however, any given number can appear only once – for example, 5 + 5 is not allowed. To check your answer fill in the table below with the various combinations.
1 =
2=
3=
4=
5=
6=
7=
8=
9=
10=
11=
12=
13=
14=
15=
16=
17=
18=
19=
20=
21=
22=
23=
24=
25=
26=
27=
28=
29=
30=
31=
32=
33=
34=
35=
36=
37=
38=
39=
40=
Answer:
The numbers are 1,3,9 and 27. This problem is a good exercise in getting the maximum work from a minimal number of elements (or the maximum relief from Parkinson’s symptoms from the fewest number of therapies!)
1 =1
2=3-1
3=3
4=3+1
5=9-3-1
6=9-3
7=9-3+1
8=9-1
9=9
10=9+1
11=9+3-1
12=9+3
13=9+3+1
14=27-9-3-1
15=27-9-3
16=27-9-3+1
17=27-9-1
18=27-9
19=27-9+1
20=27-9+3-1
21=27-9+3
22=27-9+3+1
23=27-3-1
24=27-3
25=27-3+1
26=27-1
27=27
28=27+1
29=27+3-1
30=27+3
31=27+3+1
32=27+9-3-1
33=27+9-3
34=27+9-3+1
35=27+9-1
36=27+9
37=27+9+1
38=27+9+3-1
39=27+9+3
40=27+9+3+1
Today’s Problem:
Fill a glass with water completely up to the rim. Then slip a penny into the glass. The water will not overflow with just one additional penny inside. Approximately how many pennies can you slip into the glass before the water spills over the edge?