# Use the numbers 4 4 7 8 9 10 = 740

I've got a puzzle to which I can't find the answer. Form the number $740$ using only these numbers:

$4$ $4$ $7$ $8$ $9$ $10$

And these operators: $+$ $-$ $*$ $/$ $($ $)$

• Is it necessary to use all of them? Are we allowed to concatenate digits (e.g., use two 4s to make 44)? – Gareth McCaughan Apr 4 '17 at 16:59
• en.wikipedia.org/wiki/Countdown_(game_show) – Wossname Apr 4 '17 at 22:56
• As an "answerer" pointed out, in the title 7 ate 9 (7 8 9... Classic)... title/question mis-match. – WernerCD Apr 4 '17 at 23:03
• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Apr 10 '17 at 16:44

Voila:

4 * ((8 + 7) * (9 + 4) - 10)

Solved by manually trying multiplying together pairs of added numbers then figuring out how to correct the error using the remaining terms.

Using a small program, I've identified 272 expressions, many of which are simply commutative transformations of each other.

(9*10+7-4)*8-4

Also solved by hand.

((4*7)+9)*(8/4)*10

Solved in head - nostalgic - I used to do this (make up my own puzzles of this nature) all the time when I was younger using the telephone numbers in the church bulletin in order to pass time.

-rC

I was hoping to find a solution that kept the numbers in order, but I couldn't think of one.

(9 * (8 + 4/4) - 7) * 10

My strategy:

keep 10 to the side and use the rest of the numbers to hit 74, then multiply by 10

I will answer to this question in steps:

1) Add numbers upto second last digit
2) Add numbers upto last digit
3) now add result of step 1 and step 2
4) multiply that result with last digit

Wanted to see if it were possible without scrambling the numbers

but the closest I could get was a disappointing:
744 = -4 - (-4 * 7) + (8 * 9 * 10)

Or If I resist the urge to pointlessly complicate:

744 = -4 + (4 * 7) + (8 * 9 * 10)

• I think the double-negative can be simplified into just an addition? – Niet the Dark Absol Apr 5 '17 at 12:21
• @NiettheDarkAbsol Well. Probably... but I have a natural gift for complicating things that I don't want to waste! (edited) – Brent Hackers Apr 5 '17 at 12:52
• You still need the - at the start though ;) – Niet the Dark Absol Apr 5 '17 at 13:59
• As long as unary negation is allowed: 4*( -4 + 7*( 8 + 9 + 10 ) ) = 740 – Paul Apr 5 '17 at 15:30
• @Paulpro Simply awesome... +1 – Brent Hackers Apr 6 '17 at 6:51