# DAY 190:

Today’s 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

Up until now, it has been possible to make every target number from 1 through to 9 with seven 7’s, so for today’s 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?

Make 190 Challenge

Can you arrive at 190 by inserting 1, 2, 8 and 18 into the gaps below?

(◯+◯)×(◯+◯) = 190