# Ane and her block toys

Ane is a very smart kid.
She has 9 number blocks [1] to [9], and 2 operation block [+] and [x].
Today She is playing with her blocks.
She is so happy after arranging her blocks,
then perform the math operation, the result is 100000.

She even can create 2 operations.

[4][8][x][5][6][+][9][7][3][1][2] = 100000
[3][x][4][1][6][+][9][8][7][5][2] = 100000


She show it to her mother, then her mother challanges her to rearrange her blocks.
The result will still 100000, but she have to use 6 number blocks for multiplication, before addition.

What will her arrangement look like ?

Note : No other operation, just 1 multiplication and 1 addition.

• Ane is smarter than me .. v.v – lois6b Oct 26 '16 at 7:12
• I want to congratulate everybody on the restraint they showed in not using <kbd>1</kbd> for blocks. – Mr Lister Oct 26 '16 at 12:18

## 3 Answers

NOTE: This answer was found by a computer program.

For 3 digits x 3 digits + 3 digits:

158*627+934 = 100000
[1][5][8][x][6][2][7][+][9][3][4]
And if you consider the same numbers in different order a different arrangement (as @Rubio pointed out):
[6][2][7][x][1][5][8][+][9][3][4]

For 2 digits x 4 digits + 3 digits:

27*3698+154 = 100000
[2][7][x][3][6][9][8][+][1][5][4]
And if you consider the same numbers in different order a different arrangement (as @Rubio pointed out):
[3][6][9][8][x][2][7][+][1][5][4]

For 1 digit x 5 digits + 3 digits:

There are no such arrangements

• how come this was accepted but not upvoted? (+1/0 with my vote by the time of this comment) – lois6b Oct 26 '16 at 8:13
• I hope that it was coded in Ana – durum Oct 26 '16 at 15:13

There are four solutions (found via computer):

[1][5][8][×][6][2][7][+][9][3][4] = 100000     (158 × 627 + 934)
[2][7][×][3][6][9][8][+][1][5][4] = 100000     (27 × 3698 + 154)
[3][6][9][8][×][2][7][+][1][5][4] = 100000     (3698 × 27 + 154)
[6][2][7][×][1][5][8][+][9][3][4] = 100000     (627 × 158 + 934)

• I would consider A x B + C is the same as B x A + C in which case there are two. – oleslaw Oct 26 '16 at 7:50
• mathematically they are, but she's playing with blocks. i considered order relevant. – Rubio Oct 26 '16 at 7:53
• I think you are right so I added your reasoning to the accepted answer for completeness. – oleslaw Oct 26 '16 at 8:08

The answer is:

627*158+934

... which is equal to 100000.