# day/dydd 138 at 7puzzleblog.com

T he Main Challenge

The two sections below both contain ten letters, A-J; each of which has a multiplication calculation assigned to it:

• Section 1

C:10×2  J:4×3  F:8×5  D:3×3  I:3×2  G:7×4  B:5×4  H:9×4  E:10×3  A:6×4

• Section 2

B:12×2  D:6×1  G:8×3  J:5×2  E:6×5  I:6×6  H:8×6  A:9×2  F:7×2  C:6×3

Which is the only letter that contains the same answer in both sections?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Find three different numbers that have a sum of 77?

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 TEN ways of making 138 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 138 by inserting 2, 6, 10 and 15 into the gaps on each line?

•  ◯×◯–◯×◯ = 138
•  (◯+◯–◯)×◯ = 138
•  ◯²+double◯+◯+◯ = 138