# DAY/DYDD 77: The Main Challenge

The two sections below both contain eight letters, A to H.  Each letter has a calculation attached.  Which is the only letter to have the SAME answer in BOTH sections?

• Section 1

E:8×3   B:30÷2   H:15+3   A:6×6   G:36÷3   C:40–20   F:18+12   D:32–8

• Section 2

G:10+6   F:6×5   C:9×4   E:40÷2   H:30–18   A:15+9   D:30–12   B:120÷4 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which two numbers have a difference of 36? 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 FOUR ways of making 77 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers

The Target Challenge

Can you arrive at 77 by inserting 2, 4, 5 and 7 into the gaps on each line?

•  ◯×(◯+◯+◯) = 77
•  ◯²+◯×(◯+◯) = 77
•  ◯×double(◯+◯)+ = 77 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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