# DAY/DYDD/GIORNO/NAP 91: T he Main Challenge

What is the total of all the square numbers from 1-100 inclusive? 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 contain the following fourteen numbers:

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

List FIVE sets of three different numbers that all have a sum of 100. 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 FIVE ways of making 91 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 91 by inserting 2, 4, 5 and 9 into the gaps on each line?

•  (+◯)×(◯+◯) = 91
•  ◯³+◯×(◯–◯) = 91
•  ◯²×◯×√◯–◯ = 91   