# day/dydd 151 at 7puzzleblog.com T he Main Challenge

Solve all four lines arithmetically by filling the 16 gaps below with digits 0-9, but each digit must only be inserted a maximum of TWICE in the whole challenge:

◯  +  ◯   =     8     =   ◯  +  ◯
◯  +  ◯   =     3     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     1     =   ◯  ÷  ◯

Enjoyed this? Click Mathelona for details of our pocket book challenges. 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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the sum of the multiples of 12? 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 151, in FIVE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 26 and 9 once each, with + – × ÷ available, find the SIX numbers it is possible to make from the list below:

1    3    6    10    15    21    28    36    45    55    66

#TriangularNumbers The Target Challenge

Can you arrive at 151 by inserting 469 and 11 into the gaps on each line?

•  ◯²+◯×◯+◯ = 151
•  ◯²+◯×◯–◯ = 151   