# What letter should replace the '?'

A question was asked in a mental ability test (which ended on Saturday).

What letter should replace the question mark '?'

Can you solve it?

• Do we know from context (e.g., previous questions in similar tests) whether this is likely to have anything to do with the letters as letters? (E.g., "letters at the top are all second letters of names of infectious diseases" does, whereas "letters at the bottom have prime numbers of curved segments" doesn't.) Commented Jun 16, 2016 at 13:27
• (I don't mean to imply that this question is necessarily about classifying letters at all; those were just examples.) Commented Jun 16, 2016 at 13:28
• @GarethMcCaughan There was nothing mentioned which would help to understand the question better. It was under the IQ part of the test, so it implies that it had to do with the visual cues and patterns given in the image. You can post your answer considering letters as 'letters; as you said. I will add my approach after a few days :) Commented Jun 16, 2016 at 13:36
• I'm sorry if I got your hopes up -- I don't have an answer, not yet at any rate. Commented Jun 16, 2016 at 13:39
• Yeah. Except that actually Jeremy's answer looks convincing enough that I've little motivation to look for a different one. Commented Jun 16, 2016 at 14:50

My guess is that it is:

an L. If you take the first letter at the top, append the middle string "age", and combine it with the last letter on the bottom string, you get words, and L is the only letter which fits.

Bagel Pager Lager Cagey Waged Eager Rages

• Hmm, a very interesting and logically sound answer. +1 Commented Jun 16, 2016 at 13:40
• Never heard of cagey, that's a great word: reluctant to give information owing to caution or suspicion. Commented Jun 16, 2016 at 15:34
• @Jeremy Your answer is marked as correct, as it's simple and brilliant :) Commented Jun 16, 2016 at 17:27
• @CoreyOgburn No, I don't. But yes, I'll send an email to the contest organisers asking about the solutions of the questions asked in two rounds. Hopefully they'll provide it. Commented Jun 16, 2016 at 18:20
• @ABcDexter Thanks for the check mark! Please comment if you receive the correct answer, and feel free to provide my solution to them if they'd like one. Commented Jun 16, 2016 at 20:17

I went with the first thing that made numbers fit together:

The top triangle is three letters wide. The bottom triangle is five letters wide. You can align the top triangle so that it "funnels" three letters into one of the ones in age, and the top triangle so that it funnels five.

Assign each letter of the alphabet a number, from 1 to 26. Now place both triangles with the pointy end pointing towards A. That is B+P+L on the top and S+R+D+Y+R. This adds up to 5 and 6 (modulo 26). 6 - 5 = 1 = A.

Repeat for G. The letters above add up to 12, and the letters below add to 5. 12 - 5 = 7 = G.

Solve for E. It adds up to: 5 on top, and 18 + ? on the bottom. Caveat: there are two solutions to this approach: M and W (so that the operations are either 5-0 or 10-5). Which is pretty cool IMO and seems better than coincidence, but I can't come up with a way to choose one over the other. Which probably dooms my answer.

• I was going for a similar approach. Commented Jun 16, 2016 at 16:33
• We could both be wrong. @Jeremy 's answer is much more simple. But it could possibly be an open puzzle with more than one way to solve... afterall, no rules were given. Commented Jun 16, 2016 at 16:35
• And this is why using these sorts of tests as measures of "intelligence" is total bunk. Commented Jun 16, 2016 at 18:20
• @fluffy you're probably right, actually the test was free of cost and i was getting bored :/ Commented Jun 17, 2016 at 3:02
• @fluffy entertaining bunk Commented Jun 17, 2016 at 12:22