An expression is formed using the numbers 7, 16, 25, and 27 according to the following rules.

Each of the four numbers is used exactly once.

The four numbers may be used in any order.

Exactly three operations are used; each one is either + or x. (Addition or multiplication)

An unlimited number of parentheses may be used.

No two distinct expressions have the same simplified value. The two expressions below are not distinct, and therefore must be counted as only one value. What is the greatest number of distinct values, including the one below, that can be obtained when building expressions following these rules?

\((7+16+27) \times 25 = 25 \times (27+7+16)\)

BillyBobJoeJr Jul 20, 2020

#1**+1 **

Why don't you list all the ones that you can find and invite people to find more?

Melody Jul 23, 2020

#2**+1 **

There is only 3 signs plus brackets

These are some options to think about.

There are too many to just count them, you need a method.

All times - easy 1 way

All plus - easy 1 way

1 times and 2 plus 4C2+2*4C2+4+4C2 = 6+12+4+6 = 28 Maybe

2 times and 1 plus 4+6+6= 16 Maybe

1+1+28+16 = 46 maybe

Discuss your thoughts

Melody Jul 23, 2020

#3**+1 **

Well, that is good logic, but we can make use of parintasees to make even more values.

BillyBobJoeJr
Jul 25, 2020