T he Main Challenge
The seven musical letters, A-G, in the three sections below each contain an addition calculation. Only one letter has the same answer in all three sections, which one?
- Section 1
E: 11+6 G: 7+7 C: 10+4 A: 13+6 B: 9+4 F: 8+8 D: 9+3
- Section 2
A: 11+5 C: 13+5 F: 9+6 E: 15+3 D: 6+6 B: 8+5 G: 7+6
- Section 3
C: 11+3 B: 11+2 D: 7+4 G: 14+1 F: 12+3 E: 14+3 A: 15+4
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.
The 1st & 4th rows of the playing board contain the following fourteen numbers:
2 3 9 10 14 15 22 32 35 40 44 54 60 72
Which two separate numbers, when 9 is added to them, both become square numbers?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.
For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).
There are FOURTEEN different ways to make 246 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 2, 5 and 10 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 246 by inserting 3, 4, 5, 6 and 7 into the gaps below?
- (◯×◯+◯×◯)×◯ = 246
Answers can be found here.
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