# day/dydd 156 at 7puzzleblog.com T he Main Challenge

Can you make all four lines work out arithmetically by placing the digits 0-9 into the 16 gaps in our latest Mathelona challenge?

◯  +  ◯   =    10    =   ◯  +  ◯
◯  +  ◯   =     1     =   ◯  –  ◯
◯  +  ◯   =    15    =   ◯  ×  ◯
◯  +  ◯   =     5     =   ◯  ÷  ◯

Note that each digit can only be inserted a maximum of TWICE. 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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which FOUR different numbers have a sum of 100? 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 (4+1+1+1).

Show how you can make 156, in SIX different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable The Target Challenge

Can you arrive at 156 by inserting 235 and 7 into the gaps in each line below?

•  ◯²×◯+(◯–◯)² = 156
•  (◯²+◯²)×(◯+◯) = 156
•  (◯+◯)²+double(◯×◯) = 156   