# DAY/DYDD 169: T he Main Challenge

Three unique digits from 1-9 must be used to arrive at the target number 18 when multiplying two numbers together and adding or subtracting the third unique number, (a×b)±c.

One way of arriving at 18 is (5×4)2.  Find the other FOUR ways it is possible to make 18.

[Note:  (5×4)–2 = 18 and (4×5)2 = 18  counts as just ONE way.] 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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which number above 20 becomes a multiple of 11 when 20 is subtracted from it? 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 169, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only FOUR numbers it’s 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 169 by inserting 1, 3, 13 and 15 into the gaps on each line?

•  ◯×(◯+◯–◯) = 169
•  (◯–◯)²+(◯÷◯)² = 169   