# day/dydd 196 at 7puzzleblog.com T he Main Challenge

Here’s a 10-step number trail involving the four arithmetical operations, some 3-digit numbers, plus fractions and percentages.

• add three hundred and eighty
• 292
• +106
• 50%
• 1/2 of this
• multiply by nine
• 1/3 of this
• 7
• divide by seven
• +7 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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is half of the highest even number? 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).

Show how you can make 196, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which FOUR numbers is it 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 196 by inserting 568 and 9 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 196
•  (◯+◯)²+(◯×half◯) = 196
•  (◯+◯)²–(²+half◯) = 196
•  ◯³+◯–(◯+double◯) = 196
•  ◯³+◯–(◯²+√◯) = 196   