# day/dydd 163 at 7puzzleblog.com T he Main Challenge

Fill the 15 gaps below with the numbers 1-15, once each, so all five lines work out:

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

The concept behind this challenge is similar to my Mathelona number puzzles, so please feel free to click the link for details of my popular pocket book of 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which 2-digit number, when 4 is subtracted from it, becomes a multiple of 9? 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 (or 4+1+1+1).

Show how you can make 163, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only FOUR numbers it’s 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 163 by inserting 579 and 20 into the gaps on each line?

•  ◯×+◯× = 163
•  ◯×+◯+double = 163   