# day/dydd 34 at 7puzzleblog.com

Th e Main Challenge

In this addition-only Mathelona-style puzzle, place the following 12 numbers into the 12 gaps so that all four lines work out:

1    1    2    3    4    4    5    5    6    8    9    10

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

From the list, what is the sum of the even 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 FOUR ways of making 34 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 34 by inserting 2, 3, 5 and 8 into the gaps on each line?

•  ◯×+◯× = 34
•  ◯×◯–◯× = 34
•  (◯–×◯+ = 34