# day/dydd 246 at 7puzzleblog.com

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 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 25 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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