# day/dydd 314 at 7puzzleblog.com

The Main Challenge

Today’s task using the excellent, addictive American maths card game 24game is to try and arrive at the target answer of 24 from each of the following seven groups of numbers. In each calculation, all four digits must be used exactly once each, with + – × ÷ available.

But it is impossible to reach 24 with one of these seven groups:

•    2    2    2    3
•    2    2    2    4
•    2    2    2    5
•    2    2    2    6
•    2    2    2    7
•    2    2    2    8
•    2    2    2    9

Which one?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

What is the sum of the multiples of 7?

The Factors Challenge

Which of the following numbers are factors of 314?

4    6    8    10    12    14    16    18    None of them

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 314 by inserting 4, 9, 16, 25 and 36 into the gaps below?

•  (◯+◯)×(◯–◯)–◯ = 314