# day/dydd 120 at 7puzzleblog.com

T he Main Challenge

Your task is to make the target number of 10 by adding together five numbers. You are limited to using 1 to 5, but these can be used any number of times in each sum.

One way to make 10 is 5+2+1+1+1 (or 52111); can you find the other FIVE ways?

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 & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of the multiples of 6?

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 just TWO ways of making 120 when using Lagrange’s Theorem. Can you find them both?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which THREE numbers are NOT possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 120 by inserting 3, 4, 5 and 6 into the gaps on each line?

•  (◯+√◯)×◯×◯ = 120
•  (◯×◯)²×◯÷◯ = 120
•  (double(◯+◯)²)×◯÷◯ = 120