4
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In the Digital Font shown below, each letter is made up of line segments. For example letter A has 6, B has 7, C has 4 segments and so on.

Question 1 ( Easy)

Which english number, when spelled out (with capital letters) has the same total number of segments as the number itself?

( It is no fun going through each number. There is some logic here.)

Example : ONE has 6+5+5 = 16 segments

Question 2 ( Not so easy)

Which 2 numbers when added together give you a number same as the total number of segments in those 2 numbers? Ignore + sign segments. This must be other than the first number

Example : ONE + ONE = 2 But ONE + ONE = 32 segments not the right answer of course

Surprisingly, I think both answers are unique. No programming please.

enter image description here

NO PARTIAL ANSWERS PLEASE. BECAUSE ONE IS EASY

This puzzle can be linked to

What world is he thinking of?

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  • $\begingroup$ Just to clarify, are M and W intended to be 5 or 6 segments each? (They have 6 line segments but two appear to be joined into a single piece.) $\endgroup$ – Gareth McCaughan Mar 9 at 13:29
  • $\begingroup$ They need to be 6 each $\endgroup$ – DEEM Mar 9 at 13:42
5
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1:

THIRTY NINE: 3+5+2+6+3+3 (22) + 5+2+5+5 (17) = 39

2:

THIRTY EIGHT (22+21=43) + FORTY EIGHT (22+21=43) = 86

Some related curios:

THIRTY + NINE = THIRTY NINE
TEN (3+5+5=13) + FIVE (4+2+4+5=15) = FIFTEEN (4+2+4+3+5+5+5=28)
SEVEN (5+5+4+5+5=24) - FOUR (4+6+5+6=21) = 3

Method:

I first calculated each number ONE through NINE, TEN through NINETEEN, and then TWENTY, THIRTY, etc...

 one 6+5+5=16 (15)
 two 3+6+6=15 (13)
 three 3+5+6+5+5=24 (21)
 four 4+6+5+6=21 (17)
 five 4+2+4+5=15 (10)
 six 5+2+4=11 (5)
 seven 5+5+4+5+5=24 (17)
 eight 5+2+6+5+3=21 (13)
 nine 5+2+5+5=17 (8)
 ten 3+5+5=13
 eleven 5+3+5+4+5+5=27
 twelve 3+6+5+3+4+5=26
 thirteen 3+5+2+6+3+5+5+5=34 
 fourteen 4+6+5+6+2+5+5+5=38
 fifteen 4+2+4+3+5+5+5=28
 sixteen 5+2+4+3+5+5+5=29
 seventeen 24+3+15=42
 eighteen 21+15=36
 nineteen 17+3+15=35
 twenty 3+6+5+5+3+3=25
 thirty 3+5+2+6+3+3=22
 forty 4+6+6+3+3=22
 fifty 4+2+4+3+3=16
 sixty 5+2+4+3+3=17
 seventy 5+5+4+5+5+3+3=30
 eighty 5+2+6+5+3+3=24
 ninety 5+2+5+5+3+3=23
 hundred 5+5+5+6+6+5+6=38
For the single number, nothing less than twenty works so it must be a lexical composite, and a bit of reasoning tells which roughly where to be aiming.

For the sum, again you can get a rough idea. I hit upon thirty+forty=44. 44 is 26 short of 70, so to add the next numbers we need DF(a+b)=a+b+26. I calculated the excess for each single digit (the number in brackets), and a=b=8 gives my result.

And now, THIRTY=30-8, and NINE=9+8.

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  • $\begingroup$ Other than the first number. $\endgroup$ – DEEM Mar 9 at 14:15
  • $\begingroup$ Did you go through each number or could you find the logic behind? If so, what is it? $\endgroup$ – Amit Hagin Mar 10 at 23:36
  • $\begingroup$ @AmitHagin; I've added an explanation $\endgroup$ – JMP Mar 11 at 4:33
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Answers for Question 1:

39

Answers for Question 2:

2 and 46
2 and 53
3 and 52
3 and 58
4 and 54
4 and 57
5 and 49
6 and 42
6 and 48
7 and 54
7 and 57
8 and 46
8 and 53
9 and 30
9 and 45
10 and 36
10 and 41
13 and 52
13 and 58
15 and 46
15 and 53
16 and 46
16 and 53
18 and 40
20 and 42
20 and 48
22 and 40
23 and 59
23 and 64
23 and 67
24 and 63
26 and 49
27 and 63
28 and 40
29 and 46
29 and 53
30 and 9
32 and 42
32 and 48
33 and 46
33 and 53
36 and 10
36 and 43
38 and 42
38 and 48
39 and 39
40 and 18
40 and 22
40 and 28
41 and 10
41 and 43
42 and 6
42 and 20
42 and 32
42 and 38
43 and 36
43 and 41
45 and 9
46 and 2
46 and 8
46 and 15
46 and 16
46 and 29
46 and 33
48 and 6
48 and 20
48 and 32
48 and 38
49 and 5
49 and 26
52 and 3
52 and 13
53 and 2
53 and 8
53 and 15
53 and 16
53 and 29
53 and 33
54 and 4
54 and 7
57 and 4
57 and 7
58 and 3
58 and 13
59 and 23
63 and 24
63 and 27
64 and 23
67 and 23

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  • $\begingroup$ 20+42 and 20+48 also work $\endgroup$ – JMP Mar 9 at 15:12
  • $\begingroup$ 30+16 isn't a solution $\endgroup$ – JMP Mar 9 at 15:20

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