# DAY/DYDD/PÄIVÄ/NAP 92

T he Main Challenge

By following these rules, list SEVEN different positive whole numbers that total 100:

• each number must be at least 4 away from its nearest neighbour,
• the list must contain at least three square numbers.

Can you find at least one solution?

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

What is the sum of the multiples of 4?

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 THREE ways of making 92 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

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

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 92 by inserting 2, 4, 10 and 12 into the gaps on each line?

• ◯×◯×◯+◯ = 92
• ◯²–(◯+◯)÷◯ = 92
• ◯×(◯–◯)–= 92