# day/dydd 190 at 7puzzleblog.com T he Main Challenge

This is the 3rd, and final, part of a number puzzle posted initially on DAY 10, then on DAY 180, and made famous by French writer, George Perec.

The challenge involves using seven 7′s (7 7 7 7 7 7 and 7) once each, with + – × and ÷ available, to make various target numbers.

For instance, to make 9 in the previous challenge on DAY 180, you could have done:

• [7 + (7÷7) + (7÷7)] × (7÷7) = 9

In previous challenges, we made every target number from 1 through to 9 with seven 7’s, so for today’s time-consuming task:

Part 1:  Show how to make all target numbers from 10 through to 19.

Part 2: Which is the first number after 19 that is impossible to make with seven 7’s? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

Which two numbers have a difference of 13? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 190, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable The Target Challenge

Can you arrive at 190 by inserting 4, 5, 6 and 14 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 190
•  (◯×◯+◯)×◯ = 190
•  ◯²–◯×(◯–◯) = 190   