# day/dydd 220 at 7puzzleblog.com T he Main Challenge

The ten letters, A-J, in the following two sections each contains a calculation.  Which is the only letter that has the same answer in both sections?

• Section 1

E:6÷6   I:5+1   G:3+2   A:102   J:4+3   C:5×1   F:6÷3   B:84   H:9÷3   D:4×2

• Section 2

H:43   A:6÷1   I:3×3   B:61   F:64   J:8÷2   E:5×2   G:4×1   D:93   C:2+1 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 3rd & 4th rows of the playing board contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the difference between the two largest odd 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 NINE different ways to make 220 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is 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 220 by inserting 51020 and 30 into the gaps on each line?

•  (◯+◯)×◯+◯ = 220
•  (◯+◯)×◯–◯ = 220
•  ◯×◯+◯–double◯ = 220
•  (◯+◯)²–half(◯–◯) = 220
•  ◯×(◯÷◯)³–◯ = 220   