Same blocks- different numbers

[Jingle47]

Suppose you have the following blocks...
1
2
3
5
7
+
-
X
log
%
(
)
The object is to form expressions that
equal all the integers from 1 through 100.
for example if you put the 1 block in
front of you you would have 1. if you put the
2 to the right of the 1 you would
have 12 if you put down the three blocks 1+3
you would have 4.
1)..............can you can form all 101 integers from 1 to 100?
2)What is the least numberof blocks you must use to form all the integers 1 through 101?

HINT: you can place the blocks any way you want but you must obey order of operations...
if you place the 5 to the right of the 2 but raised up a little bit you would have 2^5=32.
Also you can turn the blocks however you want as well.

[Jingle47]

Noone ever tries to do my puzzles!!!
ARe they that bad?
ARe they too complicated or just trivial?

[Nobody]

aww... don't feel bad, ill go to work on in

------------------
I am Nobody
Nobody is perfect
Therefore, I am perfect

[Jingle47]

5^3-27=98
5^3-27+1=99
Now you only have to do 98 more.

[HappyMutant]

May as well give it a good kick.

code:

---

1 = 1


2 = 2


3 = 3


4 = 5 - 1


5 = 5


6 = 3 x 2


7 = 7


8 = 2 ^ 3


9 = 3 ^ 2


10 = 5 * 2


11 = 7 + 5 - 1


12 = 7 + 5


13 = 7 + 5 + 1     the second '+' is a sideways 'x'


14 = 7 x 2


15 = 3 x 5


16 = 3 x 5 + 1


17 = 3 x 5 + 2


18 = (5 + 1) x 3 


19 = 5 ^ 2 - 7 + 1


20 = 7 x 3 - 1


21 = 7 x 3


22 = 7 x 3 + 1


23 = 7 x 3 + 2


24 = 3 x (7 + 1)


25 = 5 ^ 2


26 = 5 ^ 2 + 1


27 = 3 ^ (2 + 1)


28 = 5 ^ 2 + 3


29 = 7(3) + 5 + 3  again, sideways 'x'


30 = 3(7 + 2 + 1)  ditto

---

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Brunch - you'll love it. It's not quite breakfast, it's not quite lunch; but it comes with a slice of cantaloupe at the end.

[robichelli]

code:

---

31=(2^5)-1


32=2^5


33=(7x5)-2


34=(7x5)-1


35=7x5


36=(7x5)+1


37=(7x5)+2


38=(2^5)+5+1 x was turned on its side

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[This message has been edited by robichelli (edited 04-01-2002 04:11 PM).]

[Chuck]

Your 38 uses 5 twice.

38 = 15 + 23



[This message has been edited by Chuck (edited 04-01-2002 09:06 PM).]

[Chuck]

39 = 2^5 + 7

[Chuck]

40 = (7+1) x 5

[Chuck]

41 = 7^2 - (3+5)

[Chuck]

42 = 35 + 7

[The Dark]

Don't need any pesky sideways Xs
13 = 13
29 = 31 - 2
30 = 27 + 3

[Zealot]

43=7^2 - (5 + 1)

[Zealot]

44 = 75 - 31 or 7^2 - 5
45 = 7^2 - (3 + 1)
46 = 7^2 - 3




[This message has been edited by Zealot (edited 04-01-2002 07:26 PM).]

[CrystyB]

Am i the only one that likes MATH? How do you people dare trash it so hard???

There are only 100 integers between 1 and 100, inclusive..
What base is the log?
When a block is given X, one cannot assume it is useable for addition!

[i_h8_evil_stuff]

would that "X" be a sign of multiplication, or is it a variable?



------------------
The name explains it all.

[cubestudent]

47 = 7^2 + 3 - 5
48 = 7^2 - 1
49 = 7^2
50 = 7^2 + 1
51 = 51
52 = 52
53 = 53
54 = 7^2 + 5
55 = 5 * (13 - 2)
56 = 7 * (3 + 5)
57 = 57
58 = 57 + 1
59 = 57 + 2
60 = 57 + 3
61 = 73 - 12
62 = 2 * 31
63 = 7 * 3^2
64 = 71 - (5 + 2)
65 = 71 - (2 * 3)
66 = 71 - 5
67 = 72 - 5
68 = 73 - 5
69 = 71 - 2
70 = 57 + 13
71 = 71
72 = 72
73 = 73
74 = 2 * 37
75 = 75




[This message has been edited by cubestudent (edited 04-01-2002 10:08 PM).]

[Lucky Wizard]

56=53+2+1
57=57
58=5*13-7
59=57+2
60=5*12
61=53+7+1
62=57+3+2
63=7*(3^2)
64=(7+1)^2
65=71-(2*3)
66=3*(17+5)
67=73-(5+1)
68=71-3
69=71-2

[Lucky Wizard]

Just so you know, when I started typing, cubestudent's post only had the numbers up to 55.

[cubestudent]

sorry 'bout that

[SaberKitty]

code:

---

76=75+1


77=75+2


78=75+3


79=75+3+1 (2nd + is a sideways x)


80=75+3+2 (see above)

---

ha ha, i finally posted at least a few before they were already up

[Chuck]

80 = 57 + 23

Is it legal to rotate a + or × by 45°?

[Chuck]

Can we turn log upside down to make 601?

[CrystyB]

What would you do with 601? (601-1)%=6 ?

[This message has been edited by CrystyB (edited 04-01-2002 09:22 PM).]

[cubestudent]

81 = 3^(5 - 1)
82 = 5 * 17 - 3
83 = 3^(5 - 1) + 2
84 = 7 * 12
85 = 13 + 72
86 = 15 + 73 - 2
87 = 15 + 72
88 = 15 + 73

[edited to remove 4's (and change a 2 to a 3) blech!]



[This message has been edited by cubestudent (edited 04-01-2002 09:41 PM).]

[Chuck]

All true, but we don't have a 4 block.

[Chuck]

601 could be useful if we can angle the minus sign to make a division sign.

[Zealot]

You could use 5 - 1 instead for 81 and 83.

[This message has been edited by Zealot (edited 04-01-2002 09:26 PM).]

[cubestudent]

oops

[Chuck]

We can rotate the percent sign to look like zero divided by zero which can equal anything. All numbers can be expressed with one block.

[Zealot]

82 = 5^2 * 3 + 7

[Zealot]

86 = 71 + 3 * 5

[Zealot]

cubestudent: 82 should be -3, not -2.

[cubestudent]

argh! doggone it!

[Zealot]

64, 65, 69, and 70 also have 4's in them, so here are some versions without a 4:
64 = (7 + 1)^2
65 = 57 + 2^3
69 = 71 - 2
70 = 75 - (2 + 3)

[Chuck]

89 = 57 + 32

[Jingle47]

You all are doing so well.....
I guess 1 through 100 is only 100 numbers...I always hate counting.
If you want to know about turning blocks, read the first couple posts.
Has anyone worked on the second part of the problem?
In other words how many blocks can you do without and still make all 100 numbers ?

PS chuck I got my package today....I am already loving Flatterland!!
------------------
I AM THE SMARTEST GUY ON THE BLOCK!
-Psst! "He lives in a cul-de-sac"

[This message has been edited by Jingle47 (edited 04-01-2002 11:38 PM).]

[Chuck]

Yeah, Flatterland is good.

90 = (21-3) × 5

[Chuck]

91 = 75 + 2^(3+1)

[mikegoo]

92=127-35