Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make the statement true.
Hint
How can we figure out a way to make the two-digit number not have a decimal?
Answer
Number of Unique Solutions: 26
1: 2% of 650 = 13
2: 2% of 850 = 17
3: 4% of 925 = 37
4: 4% of 950 = 38
5: 5% of 260 = 13
6: 5% of 280 = 14
7: 5% of 320 = 16
8: 5% of 340 = 17
9: 5% of 360 = 18
10: 5% of 380 = 19
11: 5% of 460 = 23
12: 5% of 620 = 31
13: 5% of 640 = 32
14: 5% of 680 = 34
15: 5% of 720 = 36
16: 5% of 760 = 38
17: 5% of 780 = 39
18: 5% of 820 = 41
19: 5% of 860 = 43
20: 5% of 920 = 46
21: 5% of 960 = 48
22: 6% of 350 = 21
23: 6% of 450 = 27
24: 8% of 450 = 36
25: 8% of 925 = 74
26: 8% of 950 = 76
1: 2% of 650 = 13
2: 2% of 850 = 17
3: 4% of 925 = 37
4: 4% of 950 = 38
5: 5% of 260 = 13
6: 5% of 280 = 14
7: 5% of 320 = 16
8: 5% of 340 = 17
9: 5% of 360 = 18
10: 5% of 380 = 19
11: 5% of 460 = 23
12: 5% of 620 = 31
13: 5% of 640 = 32
14: 5% of 680 = 34
15: 5% of 720 = 36
16: 5% of 760 = 38
17: 5% of 780 = 39
18: 5% of 820 = 41
19: 5% of 860 = 43
20: 5% of 920 = 46
21: 5% of 960 = 48
22: 6% of 350 = 21
23: 6% of 450 = 27
24: 8% of 450 = 36
25: 8% of 925 = 74
26: 8% of 950 = 76
Source: Cecilia Calvo
Nice! I was going to submit one in a similar vein.
Using the numbers 1-9, at most one time each, fill in the boxes to create a correct sentence:
[] [] % of [] [] is [] []?
68% of 25 is 17
25 % 68 of is 17
25% of 76 is 19
76% of 25 is 19
92% of 75 is 69…
All of the solutions involve a 75 or a 25
Significantly harder:
Three digits!
Using the numbers 0-9, at most one time each, fill in the boxes to create a correct sentence:
[] [] [] % of [] [] []is [] [] [] ?
375 % 184 is 690.
348% of 175 is 609.
One answer out of many possible answers is 5% of 260 is 13
There seem to be 26 solutions.
Explanations : https://olivierdata.github.io/renigma/simple-enigma.nb.html
I got the same with my program 26 solutions.
My student got 8% of 950= 76. Is this a possible highest answer?
It is indeed!
It’s so easy I got 5% of 280=14
8% of 59=4.72
5% of 260=13 is one of the many solves for this problem
I did it this way
9% of 638 = 57
6% of 350= 21
68% of 50 is 34
6% of 350 = 21
6% = 0.06
350 * 0.06 = 21
5% of 640 is 32
5% is 0.05
640*0.05 is 32
8% of 950 = 76
2% of 650 = 13
Challenge version: Only allow digits 1-9 instead of 0-9. Then we only have 2 solutions left from the list above:
4% of 925 = 37
8% of 925 = 74
We can also rephrase this so that the percentage is 3-digit and the number is 1-digit:
▢▢▢% of ▢ = ▢▢.
I like this because it reinforces the concept of percentages above 100%. All the solutions are exactly the same! E.g. “2% of 650 = 13” becomes “650% of 2 = 13”, etc.
If you use the restricted version only allowing digits 1-9 then the two solutions are:
925% of 4 = 37
925% of 8 = 74
if you are ok with a leading 0, ==> 5 % 123 = 06