Some positive numbers add up to 19. What is the maximum product?
Following the recent decision to discontinue coursework in GCSE Mathematics, MEI have produced a discussion paper to promote general discussion that will inform national policy.
Summary:
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On a dartboard where the "doubles" count as squares and the "trebles" count as cubes how many 3 dart finishes are there starting from 501, finishing on a "double".
e.g. 20, "double" 9, "double" 20: 20 + 92 + 202 = 501
E |
F |
H |
I |
N |
O |
R |
S |
T |
U |
V |
W |
X |
1/6 |
4/3 |
7/6 |
11/6 |
1/2 |
1/3 |
5/6 |
2 |
2/3 |
3/2 |
5/3 |
1 |
13/6 |
Using these values, you will find O+N+E=1 and T+W+O=2. How much further can you go?
E |
F |
G |
H |
I |
L |
N |
O |
R |
S |
T |
U |
V |
W |
X |
3 |
9 |
6 |
1 |
-4 |
0 |
5 |
-7 |
-6 |
-1 |
2 |
8 |
-3 |
7 |
11 |
Here we again have O+N+E=1 and T+W+O=2. Now how far can you go?
It turns out that (T+W+O)+(E+L+E+V+E+N) =13. Why does this guarantee that T+W+E+L+V+E =12?
Finally, if we insist that each letter takes a different value from all other letters, how can you prove that it will be impossible to find any system in which all the integers from one to thirteen describe themselves?