# day/dydd 128 at 7puzzleblog.com T he Main Challenge

Using all four decimal numbers 0.4, 0.8, 1.2 and 3.5 once each, and with + – × ÷ available, can you arrive at the target answer of 7? 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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

What is the difference between the two prime numbers listed above? 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 is only ONE way of making 128 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 128 by inserting 4, 8, 10 and 12 into the gaps on each line?

•  ◯×◯+◯×◯ = 128
•  ◯×◯+◯²–◯ = 128
•  ◯⁴×◯÷(◯+◯) = 128   