DAY/DYDD 1:

The Main Challenge

You’re playing Roll3Dice and have rolled the numbers 1, 2 and 4 with your three dice.

This is a truly unique combination, being the only one where you can make ALL ten target numbers from 1-10, using + – × ÷ as seen below.

Can you place 1, 2 and 4 into the three gaps on each line so all ten calculations work out?

•  ◯–(◯+◯)  =  1
•  ◯×◯–◯  =  2
•  ◯÷◯+◯  =  3
•  ◯×(◯–◯)  =  4
•  ◯+◯–◯  =  5
•  ◯×◯+◯  =  6
•  ◯×◯–◯  =  7
•  ◯×◯×◯  =  8
•  ◯×◯+◯  =  9
•  ◯×(◯+◯)  =  10

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the sum of all the multiples of 5?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of 1 with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group that CANNOT make 1?

•   1   1   1
•   1   2   5
•   1   6   6
•   2   2   5
•   2   3   6
•   3   3   5
•   3   4   6

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Can you arrive at 1 by inserting 2, 4, 6 and 8 into the four gaps on each line?

•  (◯+◯)÷(◯+◯) = 1
•  (◯×◯)÷(◯+◯) = 1
•  (◯–◯)–(◯÷◯) = 1
•  (◯+◯–◯)÷◯ = 1
•  ◯²÷(◯+◯+◯) = 1

Answers can be found here.

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