# DAY 155:

The Main Challenge

Can you arrive at the target number 81 by using the five numbers 1, 2, 3, 4 and 5 exactly once each, and with + – ×  ÷ available?

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 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

List three pairs of numbers with a difference of 9.

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 (4+1+1+1).

Show how you can make 155, in SIX different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using the three digits 35 and 8 once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 155 by inserting 3510 and 11 into the gaps in each line below?

•  ◯×◯×◯–◯ = 155
•  ◯×◯+◯²×◯ = 155

Answers can be found here.

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